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Questions and Answers
When solving the equation $x + 9 = -6$, what is the value of $x$?
When solving the equation $x + 9 = -6$, what is the value of $x$?
What is the first step to solve the equation $5x - 7 = 2$?
What is the first step to solve the equation $5x - 7 = 2$?
In the equation $7(x + 4) = 6x + 24$, what step is performed after distributing on the left side?
In the equation $7(x + 4) = 6x + 24$, what step is performed after distributing on the left side?
What is the correct method to begin solving a word problem as described?
What is the correct method to begin solving a word problem as described?
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What is the last step to isolate $x$ in the equation $5x = 9$?
What is the last step to isolate $x$ in the equation $5x = 9$?
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In the step where $7x + 28 = 6x + 24$, how do you move $6x$ to the left side?
In the step where $7x + 28 = 6x + 24$, how do you move $6x$ to the left side?
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What mathematical principle is suggested to be used when solving equations involving multiple operations?
What mathematical principle is suggested to be used when solving equations involving multiple operations?
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What is the result of the equation $2(x - 1) = -3$ when solved correctly?
What is the result of the equation $2(x - 1) = -3$ when solved correctly?
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What is the slope of the line that passes through the points (3, 1) and (6, 2)?
What is the slope of the line that passes through the points (3, 1) and (6, 2)?
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What is the y-intercept of the line with the equation y = 1/3x + 0?
What is the y-intercept of the line with the equation y = 1/3x + 0?
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What is the y-coordinate of the solution for the system of equations given by y = -1/2 x – 2 and y = -7/2 x + 4?
What is the y-coordinate of the solution for the system of equations given by y = -1/2 x – 2 and y = -7/2 x + 4?
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Which equation represents the line with a slope of -2/3 that passes through the point (9, 2)?
Which equation represents the line with a slope of -2/3 that passes through the point (9, 2)?
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What is the first step to solve the system of equations -2x + y = -1 and x – 2y = -4 using substitution?
What is the first step to solve the system of equations -2x + y = -1 and x – 2y = -4 using substitution?
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What method should you use to find another point when graphing a line from the y-intercept?
What method should you use to find another point when graphing a line from the y-intercept?
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When calculating the slope using the points (1, -4) and (5, 4), what is the correct substitution after organizing the points?
When calculating the slope using the points (1, -4) and (5, 4), what is the correct substitution after organizing the points?
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Which substitution is correct when solving the equation x - 2y = -4 after isolating y from the equation y = 2x - 1?
Which substitution is correct when solving the equation x - 2y = -4 after isolating y from the equation y = 2x - 1?
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What is the solution point of the equations x = 3y and y = x + 4?
What is the solution point of the equations x = 3y and y = x + 4?
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What is the y-intercept of the line calculated from the points (3, 1) and (6, 2)?
What is the y-intercept of the line calculated from the points (3, 1) and (6, 2)?
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In the context of exponent laws, what does the equation $A^n = A * A * A * ...$ signify?
In the context of exponent laws, what does the equation $A^n = A * A * A * ...$ signify?
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To find the equation of the line using points (5, 4) and (1, -4), what is the first step you should take?
To find the equation of the line using points (5, 4) and (1, -4), what is the first step you should take?
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When using substitution to solve linear equations, what must you do with the expression after substituting it into the other equation?
When using substitution to solve linear equations, what must you do with the expression after substituting it into the other equation?
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Which of the following represents the correct general form of a linear equation?
Which of the following represents the correct general form of a linear equation?
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What is the correct final step after finding x = 2 in the given substitution example?
What is the correct final step after finding x = 2 in the given substitution example?
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How does one determine the y-intercept when graphing the equation y = -1/2 x – 2?
How does one determine the y-intercept when graphing the equation y = -1/2 x – 2?
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What is the result of $(-6p^2q)(-4p^4q^5)$?
What is the result of $(-6p^2q)(-4p^4q^5)$?
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Which expression correctly simplifies $x^5 imes x^{-2}$?
Which expression correctly simplifies $x^5 imes x^{-2}$?
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What is $2^3$ equal to?
What is $2^3$ equal to?
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What does $A^{-n}$ represent?
What does $A^{-n}$ represent?
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Which of the following represents the operation of multiplying powers?
Which of the following represents the operation of multiplying powers?
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What does the expression $A^0$ equal when A is any non-zero number?
What does the expression $A^0$ equal when A is any non-zero number?
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In the FOIL method, what do the 'Outer' terms refer to?
In the FOIL method, what do the 'Outer' terms refer to?
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What is the value of $x^{-3}$ in terms of positive exponents?
What is the value of $x^{-3}$ in terms of positive exponents?
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What does the slope of a line represent?
What does the slope of a line represent?
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If the slope of a line is 3/4, which of the following describes the movement from one point to another on the line?
If the slope of a line is 3/4, which of the following describes the movement from one point to another on the line?
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What is the standard form of writing a linear equation?
What is the standard form of writing a linear equation?
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What is the y-intercept in the equation y = 5x - 7?
What is the y-intercept in the equation y = 5x - 7?
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How would you write the equation of a line with a slope of -1/2 that passes through the point (4, 3)?
How would you write the equation of a line with a slope of -1/2 that passes through the point (4, 3)?
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What is the first step to find the slope of the line represented by the equation 2x + 4y = 8?
What is the first step to find the slope of the line represented by the equation 2x + 4y = 8?
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Which of the following equations has a slope of -4?
Which of the following equations has a slope of -4?
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When converting the equation y = 2x + 6 to standard form, what would the resulting equation be?
When converting the equation y = 2x + 6 to standard form, what would the resulting equation be?
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What is the first step to take when solving a radical equation?
What is the first step to take when solving a radical equation?
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Which of the following is a necessary step after finding a potential solution to a radical equation?
Which of the following is a necessary step after finding a potential solution to a radical equation?
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When raising both sides of a radical equation, why is it important to isolate the radical first?
When raising both sides of a radical equation, why is it important to isolate the radical first?
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If an equation is $x^2 + 6 = 2$, what is the correct way to start solving for $x$?
If an equation is $x^2 + 6 = 2$, what is the correct way to start solving for $x$?
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Which of the following steps are part of the suggested checking process after solving a radical equation?
Which of the following steps are part of the suggested checking process after solving a radical equation?
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What result would you expect if you incorrectly squared both sides of an equation before isolating the radical?
What result would you expect if you incorrectly squared both sides of an equation before isolating the radical?
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In the equation $2x + 1 = 3$, what would be the next step after isolating $2x$ to solve for $x$?
In the equation $2x + 1 = 3$, what would be the next step after isolating $2x$ to solve for $x$?
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What is the conclusion one should draw if, after isolating a radical and solving, you find a solution that makes the original radical undefined?
What is the conclusion one should draw if, after isolating a radical and solving, you find a solution that makes the original radical undefined?
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Study Notes
A Quick Algebra Review
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Simplifying Expressions: Expressions are mathematical phrases containing numbers and variables, but no equal sign. Equations contain an equal sign. Combining like terms is the primary step in simplifying expressions.
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Solving Equations: The goal in solving equations is to isolate the variable (e.g., x). This involves performing inverse operations (addition/subtraction first, then multiplication/division). Always do the same operation to both sides of the equation.
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Problem Solving: Word problems require translating English descriptions into mathematical expressions. Common steps include understanding the problem, defining variables, and creating an equation.
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Inequalities: Mathematical statements using symbols like <, >, ≤, or ≥. Solving inequalities involves using inverse operations, but remember to reverse the inequality sign if multiplying or dividing by a negative number.
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Absolute Values: The absolute value of a number is its distance from zero on the number line and is always positive. When solving equations involving absolute values, address both positive and negative possibilities.
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Linear Equations: The solutions to a linear equation graph as a straight line. Slope-intercept form (y=mx+b) is common. Slope represents the rate of change, and y-intercept is the point where the line crosses the y-axis.
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Systems of Equations: A set of two or more equations. Graphing or substitution methods can be used to find solutions to systems of equations. Solutions are points where lines intersect.
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Laws of Exponents: Rules for working with powers and exponents. Combining bases and adding exponents are common procedures.
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Quadratics: Equations with a variable raised to the second power (e.g., x²). Solving them involves factoring to make one side equal to zero. Quadratics often have two solutions.
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Rationals: Expressions involving fractions. Simplifying involves factoring, identifying values that make the denominator zero (exceptions to the domain), and canceling common factors.
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Radicals: Expressions containing roots (e.g., square roots, cube roots). Even roots cannot contain negative numbers. Odd roots are valid for negative numbers. Solving requires isolating the radical.
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