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 $\frac{2}{x} = \frac{3}{x+1}$?

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

Study Guide - Practice Questions