Podcast
Questions and Answers
What must be done to both sides of a linear inequality when dividing by a negative number?
What must be done to both sides of a linear inequality when dividing by a negative number?
- The inequality sign must be switched. (correct)
- The inequality sign remains the same.
- Both sides must be multiplied by the negative number.
- You can ignore the inequality sign.
What is the first step to take when the unknown variable is in the denominator of the equation?
What is the first step to take when the unknown variable is in the denominator of the equation?
- Divide both sides by the variable in the denominator.
- Rearrange the equation to eliminate the denominator.
- Multiply both sides by the lowest common denominator. (correct)
- Add both sides by the other side of the equation.
Which of the following is a valid linear inequality?
Which of the following is a valid linear inequality?
- $2x + 1 ext{ is greater than } 3$
- $x^2 + 3 eq 5$
- $3x - 4 ext{ less than or equal to } 5x + 1$
- 5x + 2 < 7 (correct)
In the inequality $ rac{4}{3}x - 6 < 7x + 2$, what is the initial operation needed to isolate x?
In the inequality $ rac{4}{3}x - 6 < 7x + 2$, what is the initial operation needed to isolate x?
What can be concluded if an inequality simplifies to a false statement, such as 6 < 2?
What can be concluded if an inequality simplifies to a false statement, such as 6 < 2?
What is the result of simplifying the expression $a^3 imes a^4$?
What is the result of simplifying the expression $a^3 imes a^4$?
What is the simplified form of $ rac{a^5}{a^2}$?
What is the simplified form of $ rac{a^5}{a^2}$?
According to the laws of exponents, what is $(xy)^3$ equal to?
According to the laws of exponents, what is $(xy)^3$ equal to?
What is the value of $a^0$ when $a
eq 0$?
What is the value of $a^0$ when $a eq 0$?
What is $a^{-3}$ equal to?
What is $a^{-3}$ equal to?
How do you simplify the expression $ rac{(ab)^2}{(a^2b^2)}$?
How do you simplify the expression $ rac{(ab)^2}{(a^2b^2)}$?
What does the expression $( rac{a}{b})^2$ become?
What does the expression $( rac{a}{b})^2$ become?
What is the greatest common factor (GCF) of the expression $a^4 + a^3$?
What is the greatest common factor (GCF) of the expression $a^4 + a^3$?
What is the first step for solving a quadratic equation?
What is the first step for solving a quadratic equation?
In the factorisation method for solving quadratic equations, what is the purpose of setting each factor equal to zero?
In the factorisation method for solving quadratic equations, what is the purpose of setting each factor equal to zero?
When solving simultaneous equations by substitution, what is the first step?
When solving simultaneous equations by substitution, what is the first step?
What is a necessary condition for solving simultaneous equations?
What is a necessary condition for solving simultaneous equations?
Which method involves adding or subtracting two equations to eliminate a variable?
Which method involves adding or subtracting two equations to eliminate a variable?
What step is NOT part of solving word problems using algebra?
What step is NOT part of solving word problems using algebra?
What does a literal equation represent?
What does a literal equation represent?
Which operation should be performed to isolate an unknown variable in a literal equation?
Which operation should be performed to isolate an unknown variable in a literal equation?
What is the graphical solution to simultaneous equations?
What is the graphical solution to simultaneous equations?
What is the last step in the process of solving quadratic equations?
What is the last step in the process of solving quadratic equations?
What is the result of multiplying $a^{2/3}$ by $a^{4/5}$?
What is the result of multiplying $a^{2/3}$ by $a^{4/5}$?
How would you simplify $ rac{a^{3/4}}{a^{5/6}}$?
How would you simplify $ rac{a^{3/4}}{a^{5/6}}$?
Which of the following is the correct application of the power of a power property?
Which of the following is the correct application of the power of a power property?
What is the value of $x$ in the equation $2^x = 32$?
What is the value of $x$ in the equation $2^x = 32$?
When solving the exponential equation $3^x = 81$, which method would best apply?
When solving the exponential equation $3^x = 81$, which method would best apply?
What is the highest exponent of the variable in a linear equation?
What is the highest exponent of the variable in a linear equation?
What is a possible scenario in a quadratic equation?
What is a possible scenario in a quadratic equation?
Which step is NOT part of solving a linear equation?
Which step is NOT part of solving a linear equation?
In what condition can logarithms be used to solve exponential equations?
In what condition can logarithms be used to solve exponential equations?
What is the result of simplifying $(xy)^{1/2}$?
What is the result of simplifying $(xy)^{1/2}$?
What is the first step when solving a quadratic equation using factorisation?
What is the first step when solving a quadratic equation using factorisation?
Which method involves expressing one variable in terms of the other?
Which method involves expressing one variable in terms of the other?
What ensures that a quadratic equation is balanced during manipulation?
What ensures that a quadratic equation is balanced during manipulation?
In solving simultaneous equations graphically, what does the solution represent?
In solving simultaneous equations graphically, what does the solution represent?
What is one way to check the correctness of a solution to a quadratic equation?
What is one way to check the correctness of a solution to a quadratic equation?
When solving a literal equation, what should you do to isolate the unknown variable?
When solving a literal equation, what should you do to isolate the unknown variable?
Which statement best describes simultaneous equations?
Which statement best describes simultaneous equations?
What is a key consideration when writing equations to solve word problems?
What is a key consideration when writing equations to solve word problems?
In the elimination method for solving simultaneous equations, what is the goal?
In the elimination method for solving simultaneous equations, what is the goal?
What must you remember when isolating a variable by taking a square root?
What must you remember when isolating a variable by taking a square root?
Which expression correctly simplifies according to the laws of exponents?
Which expression correctly simplifies according to the laws of exponents?
What is the result of applying the negative exponent law to the expression $a^{-3}$?
What is the result of applying the negative exponent law to the expression $a^{-3}$?
Which of the following represents the correct application of the division law of exponents?
Which of the following represents the correct application of the division law of exponents?
When simplifying the expression $(ab)^4$, what is the resulting form?
When simplifying the expression $(ab)^4$, what is the resulting form?
How can the expression $\frac{(xy)^3}{x^2 y^3}$ be simplified?
How can the expression $\frac{(xy)^3}{x^2 y^3}$ be simplified?
What is the simplified form of the expression [\frac{6a^4b^2}{3a^2b}]?
What is the simplified form of the expression [\frac{6a^4b^2}{3a^2b}]?
Which expression represents the difference of squares correctly?
Which expression represents the difference of squares correctly?
What is the significance of applying the zero exponent law?
What is the significance of applying the zero exponent law?
What is the correct expression for raising a product to a power according to the laws of rational exponents?
What is the correct expression for raising a product to a power according to the laws of rational exponents?
Which method is used to solve exponential equations when the bases cannot be made the same?
Which method is used to solve exponential equations when the bases cannot be made the same?
What does the equation $a^{m/n} imes a^{p/q}$ simplify to based on the multiplication of exponents rule?
What does the equation $a^{m/n} imes a^{p/q}$ simplify to based on the multiplication of exponents rule?
What must be done first to solve a linear equation?
What must be done first to solve a linear equation?
When can it be concluded that $x = y$ in the context of exponential equations?
When can it be concluded that $x = y$ in the context of exponential equations?
How many solutions can a quadratic equation typically have?
How many solutions can a quadratic equation typically have?
In the power of a power property, how is $(a^{m/n})^{p/q}$ expressed?
In the power of a power property, how is $(a^{m/n})^{p/q}$ expressed?
What operation should be performed to isolate the variable when solving a linear equation?
What operation should be performed to isolate the variable when solving a linear equation?
To simplify a rational exponent such as $ rac{a^{3/4}}{a^{5/6}}$, what should be done with the exponents?
To simplify a rational exponent such as $ rac{a^{3/4}}{a^{5/6}}$, what should be done with the exponents?
What must be done first when solving the inequality $ rac{3x + 1}{2}
geq 4$?
What must be done first when solving the inequality $ rac{3x + 1}{2} geq 4$?
Which inequality correctly represents the result of dividing both sides of $8 > 6$ by -2?
Which inequality correctly represents the result of dividing both sides of $8 > 6$ by -2?
In the inequality $2 - x
geq 3$, what is the correct first operation to isolate $x$?
In the inequality $2 - x geq 3$, what is the correct first operation to isolate $x$?
When manipulating the inequality $ rac{4}{3}x - 6 < 7x + 2$, what initial step is required?
When manipulating the inequality $ rac{4}{3}x - 6 < 7x + 2$, what initial step is required?
What is the correct interpretation if an equation like $6 < 2$ results from solving a linear inequality?
What is the correct interpretation if an equation like $6 < 2$ results from solving a linear inequality?
What must be done to both sides when solving the inequality $2 - x \geq 3$?
What must be done to both sides when solving the inequality $2 - x \geq 3$?
When a linear inequality such as $\frac{3x + 1}{2} \geq 4$ is presented, what is the first step to solve it?
When a linear inequality such as $\frac{3x + 1}{2} \geq 4$ is presented, what is the first step to solve it?
In solving the inequality $\frac{4}{3}x - 6 < 7x + 2$, what should be done first to isolate x?
In solving the inequality $\frac{4}{3}x - 6 < 7x + 2$, what should be done first to isolate x?
What is true about the operation performed on both sides of the inequality when dividing by a negative number?
What is true about the operation performed on both sides of the inequality when dividing by a negative number?
For the inequality $8 > 6$, what happens if both sides are divided by -2?
For the inequality $8 > 6$, what happens if both sides are divided by -2?
What does the expression $a^{-n}$ equal to?
What does the expression $a^{-n}$ equal to?
When simplifying the expression $a^5 imes a^2$, what is the result?
When simplifying the expression $a^5 imes a^2$, what is the result?
To simplify $( rac{3}{2})^3$, which law of exponents should be applied?
To simplify $( rac{3}{2})^3$, which law of exponents should be applied?
What is the simplified result of the expression $ rac{a^4 imes a^3}{a^5}$?
What is the simplified result of the expression $ rac{a^4 imes a^3}{a^5}$?
Which expression correctly applies the law of exponents to simplify $(a^2b^3)^2$?
Which expression correctly applies the law of exponents to simplify $(a^2b^3)^2$?
What is the outcome when simplifying the expression $ rac{(ab)^4}{a^2b^3}$?
What is the outcome when simplifying the expression $ rac{(ab)^4}{a^2b^3}$?
What does the zero exponent law state?
What does the zero exponent law state?
When applying the law of exponents, what is true about raising a number to a negative exponent?
When applying the law of exponents, what is true about raising a number to a negative exponent?
How can the expression $a^{1/2} imes a^{3/4}$ be simplified?
How can the expression $a^{1/2} imes a^{3/4}$ be simplified?
What is the result when the expression $( rac{2}{3})^{1/2}$ is simplified?
What is the result when the expression $( rac{2}{3})^{1/2}$ is simplified?
If $2^x = 2^5$, what can be concluded about the variable $x$?
If $2^x = 2^5$, what can be concluded about the variable $x$?
When solving the equation $3^{x} = 27$, which approach is most useful?
When solving the equation $3^{x} = 27$, which approach is most useful?
Which of the following shows the correct method for simplifying the expression $ rac{a^{5/6}}{a^{1/3}}$?
Which of the following shows the correct method for simplifying the expression $ rac{a^{5/6}}{a^{1/3}}$?
What is the characteristic of a quadratic equation?
What is the characteristic of a quadratic equation?
Which of the following options illustrates the power of a power property incorrectly?
Which of the following options illustrates the power of a power property incorrectly?
If an exponential equation simplifies to $4 < 2$ after manipulation, what does it indicate?
If an exponential equation simplifies to $4 < 2$ after manipulation, what does it indicate?
Which method should be used to solve the equation $x^2 - 5x + 6 = 0$?
Which method should be used to solve the equation $x^2 - 5x + 6 = 0$?
When solving linear equations, what should be done first?
When solving linear equations, what should be done first?
What is the correct order of operations when rewriting a quadratic equation for factorisation?
What is the correct order of operations when rewriting a quadratic equation for factorisation?
What does substituting into the second equation achieve when solving simultaneous equations by substitution?
What does substituting into the second equation achieve when solving simultaneous equations by substitution?
What must be ensured when performing operations on one side of a quadratic equation?
What must be ensured when performing operations on one side of a quadratic equation?
What is the main goal of using the elimination method in solving simultaneous equations?
What is the main goal of using the elimination method in solving simultaneous equations?
When solving a literal equation, what is the first action to isolate the unknown variable?
When solving a literal equation, what is the first action to isolate the unknown variable?
Which step is NOT part of the problem-solving strategy for word problems?
Which step is NOT part of the problem-solving strategy for word problems?
What is the graphical solution to simultaneous equations visually represented as?
What is the graphical solution to simultaneous equations visually represented as?
Why is checking the solution important after solving a quadratic equation?
Why is checking the solution important after solving a quadratic equation?
When rearranging a literal equation, what must be considered about the terms containing the unknown variable?
When rearranging a literal equation, what must be considered about the terms containing the unknown variable?
What role does dividing by common factors play in solving a quadratic equation?
What role does dividing by common factors play in solving a quadratic equation?
What must occur to the inequality sign when both sides of a linear inequality are multiplied by a negative number?
What must occur to the inequality sign when both sides of a linear inequality are multiplied by a negative number?
When solving the inequality \[\frac{3x + 1}{2} \geq 4\, what is the first step to isolate x?
When solving the inequality \[\frac{3x + 1}{2} \geq 4\, what is the first step to isolate x?
Which of the following inequalities can be solved using the same methods as linear equations?
Which of the following inequalities can be solved using the same methods as linear equations?
In the expression \[\frac{4}{3}x - 6 < 7x + 2\, which operation will help isolate x after initial simplification?
In the expression \[\frac{4}{3}x - 6 < 7x + 2\, which operation will help isolate x after initial simplification?
What can be concluded if an inequality leads to a true statement such as [4 < 5]?
What can be concluded if an inequality leads to a true statement such as [4 < 5]?
Using the multiplication of exponents, what is the result of simplifying the expression $a^5 \times a^{-3}$?
Using the multiplication of exponents, what is the result of simplifying the expression $a^5 \times a^{-3}$?
What is the simplified form of the expression $(\frac{3}{4})^{-2}$?
What is the simplified form of the expression $(\frac{3}{4})^{-2}$?
After applying the power of a power property, what is the simplified expression for $(a^2)^3$?
After applying the power of a power property, what is the simplified expression for $(a^2)^3$?
What is the correct application of the zero exponent law for the expression $b^0$?
What is the correct application of the zero exponent law for the expression $b^0$?
Which of the following represents the correct result of applying the division law of exponents to simplify $a^{10}/a^{4}$?
Which of the following represents the correct result of applying the division law of exponents to simplify $a^{10}/a^{4}$?
What will be the result of simplifying the expression $\left(\frac{2a}{3b}\right)^{2}$?
What will be the result of simplifying the expression $\left(\frac{2a}{3b}\right)^{2}$?
Applying the prime factorization method, how can the expression $a^4b^2c$ be rewritten?
Applying the prime factorization method, how can the expression $a^4b^2c$ be rewritten?
What is the result of the expression $\frac{a^5b^3}{a^2b^2}$ when simplified?
What is the result of the expression $\frac{a^5b^3}{a^2b^2}$ when simplified?
When solving a quadratic equation by factorisation, what is the correct first step?
When solving a quadratic equation by factorisation, what is the correct first step?
In solving simultaneous equations using the elimination method, which action is taken first?
In solving simultaneous equations using the elimination method, which action is taken first?
What is the main goal when solving word problems using algebra?
What is the main goal when solving word problems using algebra?
What is a crucial step to take when solving simultaneous equations graphically?
What is a crucial step to take when solving simultaneous equations graphically?
What is typically true about the variables in a literal equation?
What is typically true about the variables in a literal equation?
During the factorisation of a quadratic equation, what form should the expression be turned into?
During the factorisation of a quadratic equation, what form should the expression be turned into?
What operation must be performed to each side of a literal equation to isolate a variable?
What operation must be performed to each side of a literal equation to isolate a variable?
What must be ensured for a quadratic equation before applying the factorisation method?
What must be ensured for a quadratic equation before applying the factorisation method?
Which method can be utilized to solve systems of equations without manipulating the equations algebraically?
Which method can be utilized to solve systems of equations without manipulating the equations algebraically?
What is the result of simplifying the expression $a^{3/4} \times a^{5/6}$ using the laws of exponents?
What is the result of simplifying the expression $a^{3/4} \times a^{5/6}$ using the laws of exponents?
When rewriting the expression $\left(\frac{a}{b}\right)^{3/4}$, what is the corresponding fractional exponent representation?
When rewriting the expression $\left(\frac{a}{b}\right)^{3/4}$, what is the corresponding fractional exponent representation?
What is the value of $x$ in the equation $2^{2x} = 8$?
What is the value of $x$ in the equation $2^{2x} = 8$?
Which of the following represents the correct application of the power of a power property when simplifying $\left(a^{2/3}\right)^{4/5}$?
Which of the following represents the correct application of the power of a power property when simplifying $\left(a^{2/3}\right)^{4/5}$?
In solving the equation $3^{2x} = 27$, what method is most suitable?
In solving the equation $3^{2x} = 27$, what method is most suitable?
How can the expression $\frac{(xy)^{3/2}}{x^{1/2}y^{1/2}}$ be simplified?
How can the expression $\frac{(xy)^{3/2}}{x^{1/2}y^{1/2}}$ be simplified?
Which expression correctly simplifies according to the laws of exponents?
Which expression correctly simplifies according to the laws of exponents?
Which of the following scenarios represents a quadratic equation?
Which of the following scenarios represents a quadratic equation?
What is the highest exponent of the variable in an effective quadratic equation?
What is the highest exponent of the variable in an effective quadratic equation?
Which step is essential for checking the solution of an equation?
Which step is essential for checking the solution of an equation?
When solving the inequality $2 - x \geq 3$, what is the first step to isolate x?
When solving the inequality $2 - x \geq 3$, what is the first step to isolate x?
In the inequality $\frac{3x + 1}{2} \geq 4$, which operation must be performed to eliminate the fraction?
In the inequality $\frac{3x + 1}{2} \geq 4$, which operation must be performed to eliminate the fraction?
What must be done to the inequality sign when dividing both sides of $8 > 6$ by -2?
What must be done to the inequality sign when dividing both sides of $8 > 6$ by -2?
What type of inequality does the expression $\frac{4}{3}x - 6 < 7x + 2$ represent?
What type of inequality does the expression $\frac{4}{3}x - 6 < 7x + 2$ represent?
What is a potential outcome if an inequality simplifies to a statement like $6 < 2$?
What is a potential outcome if an inequality simplifies to a statement like $6 < 2$?
What is the primary purpose of rewriting a quadratic equation in the form $ax^2 + bx + c = 0$?
What is the primary purpose of rewriting a quadratic equation in the form $ax^2 + bx + c = 0$?
Which of the following accurately describes the elimination method for solving simultaneous equations?
Which of the following accurately describes the elimination method for solving simultaneous equations?
When solving word problems, which initial step is the most critical?
When solving word problems, which initial step is the most critical?
In what way can literal equations be effectively solved?
In what way can literal equations be effectively solved?
What do you need to ensure when solving a quadratic equation through factorisation?
What do you need to ensure when solving a quadratic equation through factorisation?
When applying substitution in simultaneous equations, which stage follows after expressing one variable in terms of the other?
When applying substitution in simultaneous equations, which stage follows after expressing one variable in terms of the other?
Which graphical representation best defines the solution to simultaneous equations?
Which graphical representation best defines the solution to simultaneous equations?
In the context of word problems, what does assigning a variable primarily achieve?
In the context of word problems, what does assigning a variable primarily achieve?
What is a vital consideration when rearranging literal equations?
What is a vital consideration when rearranging literal equations?
What is the outcome of applying the power of a power rule to the expression $\left(a^{2/3}\right)^{4/5}$?
What is the outcome of applying the power of a power rule to the expression $\left(a^{2/3}\right)^{4/5}$?
When simplifying the expression $\frac{a^{3/4}}{a^{1/2}}$, what is the resulting exponent of $a$?
When simplifying the expression $\frac{a^{3/4}}{a^{1/2}}$, what is the resulting exponent of $a$?
Which equation can be solved by equating exponents if $4^{x+1} = 16^{2-x}$?
Which equation can be solved by equating exponents if $4^{x+1} = 16^{2-x}$?
If $\frac{(x+2)^{1/3}}{(x-3)^{1/4}} = 1$, what condition must $x$ satisfy?
If $\frac{(x+2)^{1/3}}{(x-3)^{1/4}} = 1$, what condition must $x$ satisfy?
What is the key property of logarithms used to solve the equation $5^{2x} = 25^{x-1}$?
What is the key property of logarithms used to solve the equation $5^{2x} = 25^{x-1}$?
What is the correct simplification of the expression $\frac{(ab)^{2}}{a^{1}b^{3}}$?
What is the correct simplification of the expression $\frac{(ab)^{2}}{a^{1}b^{3}}$?
What is the maximum number of solutions for a quadratic equation?
What is the maximum number of solutions for a quadratic equation?
Which operation should be performed to both sides when isolating the variable $x$ in the equation $2^{x} = 8$?
Which operation should be performed to both sides when isolating the variable $x$ in the equation $2^{x} = 8$?
If $x^{2} + 5x + 6 = 0$, how can this quadratic equation be solved?
If $x^{2} + 5x + 6 = 0$, how can this quadratic equation be solved?
What is a valid reason for using the method of substitution when solving simultaneous equations?
What is a valid reason for using the method of substitution when solving simultaneous equations?
What is the result of simplifying the expression $a^5 imes a^{-2}$?
What is the result of simplifying the expression $a^5 imes a^{-2}$?
How should the expression $a^2b^3 imes a^3b^{-1}$ be simplified?
How should the expression $a^2b^3 imes a^3b^{-1}$ be simplified?
What is the result of applying the power of a power property to the expression $(a^2)^3$?
What is the result of applying the power of a power property to the expression $(a^2)^3$?
Which of the following correctly applies the division law of exponents to the expression $ rac{b^4}{b^2}$?
Which of the following correctly applies the division law of exponents to the expression $ rac{b^4}{b^2}$?
How can the expression $ rac{(3x^2y)^3}{3^2x^3y^3}$ be simplified?
How can the expression $ rac{(3x^2y)^3}{3^2x^3y^3}$ be simplified?
What does the expression $( rac{a^2}{b^3})^4$ simplify to?
What does the expression $( rac{a^2}{b^3})^4$ simplify to?
Which of the following represents the correct application of the zero exponent law for the expression $c^0$?
Which of the following represents the correct application of the zero exponent law for the expression $c^0$?
What is the simplified form of the expression $a^{-2} imes a^5$?
What is the simplified form of the expression $a^{-2} imes a^5$?
