Question 1

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

Accepted Answer

An equation that can be written in the form $$ax + b = 0$$, with $$a 
eq 0.$$

Question 2

Solve the equation $$2x - 3 = 3x + 5. $$What is the value of $$x$$?

Accepted Answer

$$x = -8$$

Question 3

Which of the following best describes the first step in solving the equation $$\frac{2x}{3} - 5 = \frac{x}{4} + 1$$?

Accepted Answer

Multiply both sides by the least common denominator (LCD), which is 12.

Question 4

Given the equation $$\frac{3x}{5} - \frac{2}{3} = \frac{1}{2}$$, what is the LCD used to clear the denominators?

Accepted Answer

30

Question 5

A rational equation is an equation that contains:

Accepted Answer

One or more rational expressions.

Question 6

Solve for $$x$$: $$\frac{2x}{7} + 5 = x - 3$$

Accepted Answer

$$x = 14$$

Question 7

Which of the following is a necessary step when solving $$\frac{5}{x+1} - \frac{3}{x-1} = 0$$?

Accepted Answer

Multiply both sides by $$(x+1)(x-1) to $$clear denominators.

Question 8

If $$C(x) = 1286.1x + 24943$$, what is the value of $$x$$ when $$C(x) = 56183$$?

Accepted Answer

$$x = 40$$

Question 9

Which of the following equations has no solution?

Accepted Answer

$$2 = -2$$

Question 10

Solve for $$x$$: $$\frac{7}{x} = \frac{49}{4x}$$

Accepted Answer

$$x = 4$$

Question 11

Which of the following is the correct solution to $$\frac{2x}{3} - \frac{5}{4} = \frac{x}{2}$$?

Accepted Answer

$$x = 5.57$$

Question 12

A company’s cost function is $$C(x) = 1286.1x + 24943. $$What does the slope $$1286.1$$ represent in this context?

Accepted Answer

The cost per unit produced.

Question 13

Which of the following is a valid step in checking your solution to a linear equation using a graphing calculator?

Accepted Answer

Set $$y_1$$ equal to the left side and $$y_2$$ equal to the right side, then find where $$y_1$$ = $$y_2.$$

Question 14

Solve for $$x$$: $$\frac{3x}{5} - \frac{2}{3} = \frac{1}{2}$$

Accepted Answer

$$x = 3.57$$

Question 15

Which of the following best describes the solution to $$\frac{2}{x} = \frac{3}{x+1}$$?

Accepted Answer

Question 16

If $$x = -1 is a $$solution to a rational equation, what must you check before accepting it as a valid solution?

Accepted Answer

That it does not make any denominator zero.

Question 17

Solve for $$x$$: $$2(x-3) = 3x + 1$$

Accepted Answer

$$x = -7$$

Question 18

Which of the following is the correct LCD for the equation $$\frac{5}{x+1} - \frac{3}{x-1} = 0$$?

Accepted Answer

$$(x+1)(x-1)$$

Question 19

If $$C(x) = 1286.1x + 24943$$, what is the cost when $$x = 30$$?

Accepted Answer

$$C(30) = 63526$$

Linear and Rational Equations: College Algebra Study Guide

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