Question 1

When solving an equation, you are trying to find the value of the variable which makes the equation a ________ statement. What is the correct word to fill in the blank?

Accepted Answer

true

Question 2

Which property justifies the following step in solving an equation: If $$a = b$$, then $$a + c = b + c$$?

Accepted Answer

Addition Property of Equality

Question 3

Solve the equation $$5(x - 1) = 8 - 2x. $$What is the value of $$x$$?

Accepted Answer

Question 4

Which of the following best describes an equation that is true for every value of the variable?

Accepted Answer

Identity

Question 5

Solve the equation $$-3(5s + 4) + 8 = 2(2s - 3) + 10. $$What is the value of $$s$$?

Accepted Answer

$$s = -1$$

Question 6

Which of the following equations is an example of a contradiction (inconsistent equation)?

Accepted Answer

$$x + 1 = x + 2$$

Question 7

Solve the equation $$x - \frac{2}{3} = 2 - \frac{1}{5}x. $$What is the value of $$x$$?

Accepted Answer

$$x = \frac{40}{13}$$

Question 8

Which of the following is NOT a possible outcome when solving a linear equation?

Accepted Answer

Exactly two solutions

Question 9

A chemical process requires the temperature $$T (in $$degrees Celsius) to satisfy the equation $$4T - 8 = 2T + 12. $$What is the required temperature?

Accepted Answer

$$T = 10$$

Question 10

Solve for $$x in $$the equation $$-4.0x + 2.8 - 1.6x = 1.3 - 5.7x + 1.4.$$

Accepted Answer

$$x = 0.6$$

Question 11

Which property allows you to multiply both sides of an equation by the same nonzero number without changing the solution?

Accepted Answer

Multiplication Property of Equality

Question 12

A medical dosage formula is given by $$7y - 1 = -1 + 7y. $$What can you conclude about $$y$$?

Accepted Answer

Any real number is a solution for $$y.$$

Question 13

Solve for $$x in $$the equation $$x - \frac{5}{8} = 4 - \frac{2}{3}x.$$

Accepted Answer

$$x = \frac{124}{11}$$

Question 14

Which of the following best describes a linear equation that has no solution?

Accepted Answer

Contradiction

Question 15

A business's profit $$P is $$modeled by the equation $$2P - 10 = 4P + 6. $$What is the value of $$P$$?

Accepted Answer

$$P = -8$$

Question 16

Which of the following equations is an identity?

Accepted Answer

$$x + 2 = x + 2$$

Question 17

A recipe requires that the sum of twice the amount of sugar $$s$$ and 5 equals 3 times the amount of sugar minus 2. Which equation models this situation?

Accepted Answer

$$2s + 5 = 3s - 2$$

Question 18

Solve for $$x in $$the equation $$3(x - 2) = 2x + 5.$$

Accepted Answer

$$x = 11$$

Question 19

Which of the following is a conditional equation?

Accepted Answer

$$2x = 6$$

Question 20

A car rental company charges a flat fee plus a rate per mile. If the total cost $$C is $$given by $$C = 50 + 0.25m$$ and you know $$C = 100$$, how many miles $$m$$ were driven?

Accepted Answer

$$m = 400$$

Solving Linear Equations in One Variable

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