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

$ax + b = 0$, where $a$ and $b$ are real numbers and $a \neq 0$

Question 1

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

Accepted Answer

$ax + b = 0$, where $a$ and $b$ are real numbers and $a 
eq 0$

Question 2

Which operation does NOT produce an equivalent equation when solving linear equations?

Accepted Answer

Multiplying both sides by zero

Question 3

Solve for $x$: $4x + 5 = 29$

Accepted Answer

$x = 6$

Question 4

Which of the following is the correct first step to solve the equation $\frac{x-3}{4} = \frac{5}{14} - \frac{x+5}{7}$?

Accepted Answer

Multiply both sides by 28, the least common denominator

Question 5

After multiplying both sides of $\frac{x-3}{4} = \frac{5}{14} - \frac{x+5}{7}$ by 28, which equation do you get?

Accepted Answer

$28\left(\frac{x-3}{4}\right) = 28\left(\frac{5}{14}\right) - 28\left(\frac{x+5}{7}\right)$

Question 6

Solve for $x$: $\frac{x-3}{4} = \frac{5}{14} - \frac{x+5}{7}$

Accepted Answer

$x = 1$

Question 7

Which of the following is a rational equation?

Accepted Answer

$\frac{5}{x} + 2 = 7$

Question 8

When solving a rational equation, what must you always check for before solving?

Accepted Answer

Restrictions on the variable by setting denominators equal to zero

Question 9

Solve for $x$: $18\left(\frac{5}{2x}\right) = 18\left(\frac{17}{18}\right) - 18\left(\frac{1}{3x}\right)$

Accepted Answer

$x = 3$

Question 10

Which of the following equations is an identity?

Accepted Answer

$7x + 9 = 9(x + 1) - 2x$

Question 11

Which equation is inconsistent?

Accepted Answer

$4x - 7 = 4(x - 1) + 3$

Question 12

A medical researcher models the average level of depression $D$ in response to a negative life event of intensity $x$ by the equation $D = 10x + 53$. If $D = 90$, what is the intensity $x$?

Accepted Answer

$x = 3.7$

Question 13

Which of the following best describes a conditional equation?

Accepted Answer

An equation that is true for at least one real number

Question 14

Given $\frac{1}{x+4} = \frac{1}{x-4}$, what are the restricted values for $x$?

Accepted Answer

$x = -4$ and $x = 4$

Question 15

Which of the following is NOT a valid step in solving a linear equation?

Accepted Answer

Multiplying both sides by zero

Question 16

If $4x - 7 = 4x - 1$, what type of equation is this?

Accepted Answer

Inconsistent equation

Question 17

Which of the following is the correct solution to $2x = 2x + 1$?

Accepted Answer

No solution

Question 18

A chemical reaction is modeled by $C = 5x + 20$, where $C$ is the concentration and $x$ is the time in minutes. If the concentration reaches $C = 45$, how many minutes have passed?

Accepted Answer

$x = 5$

Question 19

Which of the following equations is an example of a rational equation with a variable in the denominator?

Accepted Answer

$\frac{2}{x} + 3 = 7$

Chapter 1: Equations and Inequalities – Linear and Rational Equations

Study Guide - Practice Questions

Study Guide - Flashcards