Question 1

Solve the equation $2x + 3 = 7$. What is the value of $x$?

Accepted Answer

$x = 2$

Question 2

Which of the following is the solution set for $\dfrac{x}{4} = 3$?

Accepted Answer

$x = 12$

Question 3

Solve for $x$: $5x - 2 = 3x + 6$

Accepted Answer

$x = 4$

Question 4

A chemist mixes a solution containing $x$ liters of acid with $2x$ liters of water to make a $15$ liter mixture. What is the value of $x$?

Accepted Answer

$x = 5$

Question 5

Solve the equation $\dfrac{2x}{3} = 8$ for $x$.

Accepted Answer

$x = 12$

Question 6

Which value of $x$ satisfies $\sqrt{x} = 5$?

Accepted Answer

$x = 25$

Question 7

Solve for $x$: $x^2 = 49$

Accepted Answer

$x = 7, -7$

Question 8

A rectangle has a length $l$ that is $3$ units longer than its width $w$. If the perimeter is $26$ units, what is the width?

Accepted Answer

$w = 5$

Question 9

Solve the inequality $2x - 5 > 9$ and express the solution in interval notation.

Accepted Answer

$(7, \infty)$

Question 10

Which of the following is the solution to $|x - 4| = 7$?

Accepted Answer

$x = 11$ or $x = -3$

Question 11

A medical researcher finds that the number of bacteria $N$ after $t$ hours is given by $N = 1000 \cdot 2^t$. How many bacteria are present after $3$ hours?

Accepted Answer

$8000$

Question 12

Solve for $x$: $\dfrac{3x - 2}{5} = 4$

Accepted Answer

$x = 6$

Question 13

Which of the following is the solution set for $x^2 - 9 = 0$?

Accepted Answer

$x = 3, -3$

Question 14

A rectangular piece of metal is $x$ units longer than it is wide. Squares with sides $x$ are cut from the four corners, and the top is folded upward to form a box. Which equation models that the volume of the box is $75$?

Accepted Answer

$x(x + 2)(x + 7) = 75$

Question 15

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

Accepted Answer

$x = 7$

Question 16

Which of the following is the solution to $|2x - 3| = 9$?

Accepted Answer

$x = 6$ or $x = -3$

Question 17

Solve the inequality $4x + 1 \leq 9$ and express the solution in interval notation.

Accepted Answer

$(-\infty, 2]$

Question 18

A patient’s temperature $T$ (in degrees Fahrenheit) after taking medication is modeled by $T = 98.6 + 0.5t$, where $t$ is the number of hours since taking the medication. What is the temperature after $4$ hours?

Accepted Answer

$T = 100.6$

Question 19

Solve for $x$: $\dfrac{x + 2}{5} = 3$

Accepted Answer

$x = 13$

Question 20

Which of the following is the solution set for $x^2 = 16$?

Accepted Answer

$x = 4, -4$

Equations and Inequalities: College Algebra Study Guide

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