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 $$2x - 5 \u003e 9$$ 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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