Podcast
Questions and Answers
Which of the following is a solution to $x + 2 = 11$?
Which of the following is a solution to $x + 2 = 11$?
- 9 (correct)
- 7
- 11
- 13
Which of the following is true about a contradiction?
Which of the following is true about a contradiction?
- It has one solution
- It is always true
- It has infinitely many solutions
- It has no solutions (correct)
Which of the following states that if any quantity is added to (or subtracted from) both sides of an equation, the equation remains true?
Which of the following states that if any quantity is added to (or subtracted from) both sides of an equation, the equation remains true?
- Multiplication property of equality
- Subtraction property of equality
- Division property of equality
- Addition property of equality (correct)
Which of the following values would be multiplied to $\frac{3}{2}x - \frac{5}{9}x + 2$ to clear the equation of fractions?
Which of the following values would be multiplied to $\frac{3}{2}x - \frac{5}{9}x + 2$ to clear the equation of fractions?
Which of the following values would be multiplied to $0.56x - 0.98x + 0.734 = 0.43x$ to clear the equations of decimals?
Which of the following values would be multiplied to $0.56x - 0.98x + 0.734 = 0.43x$ to clear the equations of decimals?
What is the outcome of the equation $3x - 1 = 3x + 1$?
What is the outcome of the equation $3x - 1 = 3x + 1$?
Solve the equation $4x - 11 = 7$.
Solve the equation $4x - 11 = 7$.
What type of equation is $2 - 8x = 2 - 8x$?
What type of equation is $2 - 8x = 2 - 8x$?
What is the solution for $x - 1 = -x + 4$?
What is the solution for $x - 1 = -x + 4$?
What is the solution for $2 \frac{1}{2} x = 10$?
What is the solution for $2 \frac{1}{2} x = 10$?
What is the solution for $2n + 5 = n - 7$?
What is the solution for $2n + 5 = n - 7$?
What is the solution for $3x - (2x + 7) = 15$?
What is the solution for $3x - (2x + 7) = 15$?
What is the solution for $\frac{3}{8}x + 7 = 13$?
What is the solution for $\frac{3}{8}x + 7 = 13$?
What is the solution for $0.7x - 1.2 = 0.3x$?
What is the solution for $0.7x - 1.2 = 0.3x$?
What is the solution for $5(3x + 2) = 7x - 2$?
What is the solution for $5(3x + 2) = 7x - 2$?
What is the solution for $|2x + 1| = 3$?
What is the solution for $|2x + 1| = 3$?
What is the solution for $3|4x + 1| + 10 = 7$?
What is the solution for $3|4x + 1| + 10 = 7$?
What is the solution for $5|x - 1| - 2 = 23$?
What is the solution for $5|x - 1| - 2 = 23$?
In a class of 42 students, the number of boys is 12 fewer than twice the number. If the sum of the two numbers is 84, what is the equation?
In a class of 42 students, the number of boys is 12 fewer than twice the number. If the sum of the two numbers is 84, what is the equation?
One of the numbers is 40% more than another number. If the sum of both numbers is 84, what is the equation?
One of the numbers is 40% more than another number. If the sum of both numbers is 84, what is the equation?
Mrs. Hill is 4 years older than twice her son's age. If the sum of their ages is 50, what is the equation?
Mrs. Hill is 4 years older than twice her son's age. If the sum of their ages is 50, what is the equation?
For the formula $V = I R$, what is V?
For the formula $V = I R$, what is V?
For the formula $V = lwh$, what is h?
For the formula $V = lwh$, what is h?
For the equation $2x + 5y = 7$, what is y?
For the equation $2x + 5y = 7$, what is y?
For the formula $V = \frac{1}{3} S^2 h$, what is h?
For the formula $V = \frac{1}{3} S^2 h$, what is h?
Kathryn bought an aquarium that should be filled with 9 cubic feet of water. If the aquarium is 2 feet wide and 3 feet long, how high should the water fill the aquarium?
Kathryn bought an aquarium that should be filled with 9 cubic feet of water. If the aquarium is 2 feet wide and 3 feet long, how high should the water fill the aquarium?
Mr. Morgan invested $20,000 in an account earning 4.5% interest. How many years would it take for him to earn $5,400 in simple interest?
Mr. Morgan invested $20,000 in an account earning 4.5% interest. How many years would it take for him to earn $5,400 in simple interest?
Mary and her father traveled 420 miles, with three times the distance in the afternoon as in the morning. How far did they travel in the morning?
Mary and her father traveled 420 miles, with three times the distance in the afternoon as in the morning. How far did they travel in the morning?
What is a conditional equation?
What is a conditional equation?
What is a contradiction?
What is a contradiction?
What is an identity?
What is an identity?
What is an absolute value equation?
What is an absolute value equation?
Flashcards
Solution to x + 2 = 11
Solution to x + 2 = 11
x = 9
Contradiction in equations
Contradiction in equations
No solutions exist.
Addition Property of Equality
Addition Property of Equality
Adding/subtracting same value from both sides keeps the equation equal.
Clearing fractions in (3/2)x + (-5/9)x + 2
Clearing fractions in (3/2)x + (-5/9)x + 2
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Clearing decimals in 0.56x - 0.98x + 0.734 = 0.43x
Clearing decimals in 0.56x - 0.98x + 0.734 = 0.43x
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Contradiction equation example
Contradiction equation example
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Conditional equation examples
Conditional equation examples
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Identity equation example
Identity equation example
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Solving 2 1/2 x = 10
Solving 2 1/2 x = 10
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Solving 2n + 5 = n - 7
Solving 2n + 5 = n - 7
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Solving 3x - (2x + 7) = 15
Solving 3x - (2x + 7) = 15
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Solving (3/8)x + 7 = 13
Solving (3/8)x + 7 = 13
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Solving 0.7x - 1.2 = 0.3x
Solving 0.7x - 1.2 = 0.3x
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Solving 5(3x + 2) = 7x - 2
Solving 5(3x + 2) = 7x - 2
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|2x + 1| = 3
|2x + 1| = 3
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3|4x + 1| + 10 = 7
3|4x + 1| + 10 = 7
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Solving 5|x - 1| - 2 = 23
Solving 5|x - 1| - 2 = 23
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Word Problem Class Equation
Word Problem Class Equation
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Word Problem Percentage Equation
Word Problem Percentage Equation
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Word Problem Age Equation
Word Problem Age Equation
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Ohm's Law
Ohm's Law
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Volume of a Rectangular Prism
Volume of a Rectangular Prism
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Solving for y in 2x + 5y = 7
Solving for y in 2x + 5y = 7
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Conical Height Formula
Conical Height Formula
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Aquarium Height Calculation
Aquarium Height Calculation
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Investment Time Calculation
Investment Time Calculation
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Travel Morning Distance
Travel Morning Distance
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Conditional equations
Conditional equations
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Contradictions
Contradictions
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Identities
Identities
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Study Notes
Algebraic Solutions
- A solution to the equation (x + 2 = 11) is (x = 9).
- A contradiction in equations has no solutions.
- The Addition Property of Equality states that adding or subtracting the same quantity from both sides of an equation maintains equality.
Equation Manipulation
- To clear fractions in ( \frac{3}{2}x + \frac{-5}{9}x + 2), multiply by (18).
- To eliminate decimals in the equation (0.56x - 0.98x + 0.734 = 0.43x), multiply by (1,000).
Types of Equations
- The equation (3x - 1 = 3x + 1) is a contradiction, meaning no values of (x) satisfy it.
- (4x - 11 = 7) and (x - 1 = -x + 4) are conditional equations, indicating they result in a unique solution.
- The identity (2 - 8x = 2 - 8x) holds true for all (x).
Solving for Variables
- The equation (2 \frac{1}{2} x = 10) yields (x = 4).
- In the equation (2n + 5 = n - 7), the solution is (n = -12).
- The equation (3x - (2x + 7) = 15) simplifies to (x = 22).
- From ( \frac{3}{8}x + 7 = 13), the solution for (x) is (16).
- Solving (0.7x - 1.2 = 0.3x) results in (x = 3).
Variable Isolations
- The equation (5(3x + 2) = 7x - 2) simplifies to find (x = -\frac{3}{2}).
- For the absolute value equation ( |2x + 1| = 3), solutions are (x = 1) and (x = -2).
- The equation (3|4x + 1| + 10 = 7) results in no solutions.
- From the equation (5|x - 1| - 2 = 23), solutions found are (x = -4) and (x = 6).
Word Problems and Applications
- In a class of 42, where the number of boys is 12 fewer than twice the number of girls, the equation (x + 2x - 12 = 42) expresses the relationships.
- For the scenario where one number is 40% more than another and their sum is 84, the equation (x + 1.4x = 84) is used.
- Mrs. Hill's age relationship with her son can be modeled with (x + 2x + 4 = 50).
Formulas
- Ohm's Law is given by (V = IR), relating voltage (V), current (I), and resistance (R).
- Volume (V) of a rectangular prism is calculated using (V = lwh) where (l) is length, (w) is width, and (h) is height.
- The formula for solving for y in the linear equation (2x + 5y = 7) is (y = \frac{7 - 2x}{5}).
- The height (h) in conical structures can be derived from (h = \frac{3V}{S^2}), where (S) is the base area.
Geometric Applications
- To fill an aquarium measuring (2) feet wide and (3) feet long with a volume of (9) cubic feet, the height of the water must be (1.5) feet.
Interest Calculations
- Mr. Morgan's investment to earn (5400) dollars at (4.5%) interest will take (6) years.
Travel and Rate Problems
- If Mary and her father traveled (420) miles with (3) times the distance in the afternoon compared to the morning, the morning distance equals (105) miles.
Equation Types
- Conditional equations yield a finite number of solutions.
- Contradictions imply no possible solutions.
- Identities are valid for every possible value of the variable.
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Description
Test your knowledge of Algebra 1 concepts with these flashcards from Abeka's Test 2. This quiz covers essential algebraic principles including solutions to equations and properties of equality. Perfect for reviewing and reinforcing your understanding of fundamental algebra topics.
