Question 1

Which of the following equations is a linear equation in one variable?

Accepted Answer

$$x + 15 = 9x - 1$$

Question 2

What is the solution to the equation $$3(x - 4) = 2x - 1$$?

Accepted Answer

$$x = 11$$

Question 3

Which of the following best describes the equation $$2x + 3 = 5 + 4x - 2x$$?

Accepted Answer

It is a contradiction.

Question 4

Solve the equation $$0.03(z - 3) - 0.5(2z + 1) = 0.23$$ for $$z.$$

Accepted Answer

$$z = -\frac{82}{97}$$

Question 5

Which property of equality justifies the step from $$a = b to$$ $$a + c = b + c$$?

Accepted Answer

Addition Property of Equality

Question 6

A survey found that 76% of bicycle riders do not wear helmets. If there are 38.7 million riders who do not wear helmets, what is the total number of bicycle riders?

Accepted Answer

$$x = \frac{38.7}{0.76}$$

Question 7

Which equation is an identity?

Accepted Answer

$$2x + 3 = 2x + 3$$

Question 8

Solve $$-4x + 9 = 2(x - 2) + 1$$ using the x-intercept method. What is the solution?

Accepted Answer

$$x = 2$$

Question 9

Which of the following is the correct symbolic solution for $$2x - 1 = \frac{1}{2}x + 2$$?

Accepted Answer

$$x = 2$$

Question 10

A runner travels 10.1 miles in 1 hour, running part of the time at 8 mph and the rest at 11 mph. Let $$x be $$the time in hours spent running at 8 mph. Which equation models this scenario?

Accepted Answer

$$10.1 = 8x + 11(1 - x)$$

Question 11

What is the solution for $$10.1 = 8x + 11(1 - x)$$?

Accepted Answer

$$x = 0.3$$

Question 12

Which of the following best describes a conditional equation?

Accepted Answer

An equation that is true for some, but not all, values of the variable.

Question 13

If you want to eliminate fractions in the equation $$\frac{12(t-2)}{4} - \frac{12}{3}t = 12(5) - \frac{12}{12}(3-t)$$, what should you multiply both sides by?

Accepted Answer

$$12$$

Question 14

Which of the following is NOT a property of equality used to solve linear equations?

Accepted Answer

Distributive Property

Question 15

Given the equation $$\sqrt{3}(2x - \pi) + \frac{1}{3}x = 0$$, which method would be most appropriate to find the solution to the nearest tenth?

Accepted Answer

Numerical solution

Linear Equations: Concepts, Types, and Solution Methods

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