Q: Which of the following is the correct 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 correct 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

Solve for $x$: $3(x - 5) = 6x - 2x$

Accepted Answer

$x = 3$

Question 3

Which of the following steps is NOT part of the general process for solving a linear equation?

Accepted Answer

Take the square root of both sides

Question 4

Solve for $x$: $\frac{4}{3} - \frac{5}{6} = x$

Accepted Answer

$x = \frac{1}{2}$

Question 5

What is the least common denominator (LCD) for the equation $\frac{2}{x} + \frac{3}{5} = \frac{1}{3x}$?

Accepted Answer

$15x$

Question 6

Solve for $x$: $\frac{5}{2x} = \frac{1}{15} + \frac{1}{3x}$

Accepted Answer

$x = 3$

Question 7

Which of the following best describes an identity equation?

Accepted Answer

An equation that is true for all real numbers

Question 8

Determine the type of equation: $4x + 8 = 4(x + 2)$

Accepted Answer

Identity

Question 9

Solve for $x$: $\frac{1}{x+1} + 4 = \frac{17}{x-1}$

Accepted Answer

$x = 5$

Question 10

A chemical solution is diluted so that its concentration $C$ (in mg/L) after $x$ years is modeled by $C = 0.9x + 125.5$. What is the concentration after 10 years?

Accepted Answer

$C = 134.5$

Question 11

Which of the following equations is inconsistent?

Accepted Answer

$2x + 3 = 2x + 5$

Question 12

Solve for $x$: $7x - 21 = 5x + 7$

Question 13

A medical study models the average level of a drug in the bloodstream by $D = 10x + 5.2$, where $x$ is the number of hours after administration. What is the average level after 3 hours?

Accepted Answer

$D = 25.2$

Question 14

Which of the following is a conditional equation?

Accepted Answer

$3x - 1 = 2x + 4$

Question 15

Solve for $x$: $\frac{2}{x} = \frac{12}{x+2}$

Accepted Answer

$x = 2$

Question 16

If $x = 2$ is a solution to the equation $\frac{5}{x-2} = \frac{3}{x-2}$, what type of equation is this?

Accepted Answer

Inconsistent

Question 17

A company’s cost $C$ (in dollars) to produce $x$ units is given by $C = 0.03x^2 + 7.4x + 125.6$. What is the cost to produce 10 units?

Accepted Answer

$C = 229.6$

Question 18

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

Accepted Answer

Multiply both sides by 4

Solving Linear Equations and Applications in College Algebra

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