Question 1

Solve the quadratic equation $$x^2 + 4x + 8 = 0$ for x$. Which of the following is correct?

Accepted Answer

$$x = -2 \pm 2i$$

Question 2

Which of the following is the solution to the radical equation $$\sqrt{x+5} = x - 1$$?

Accepted Answer

$$x = 2$$

Question 3

Solve the compound linear inequality: $$-3 \u003c 2x + 1 \leq 7.$$

Accepted Answer

$$-2 \u003c x \leq 3$$

Question 4

Solve the absolute value equation $$|2x - 5| = 7.$$

Accepted Answer

$$x = 6,\ x = -1$$

Question 5

A chemist needs to prepare 10 liters of a 30% acid solution by mixing a 20% solution and a 50% solution. Let $$x be $$the amount (in liters) of the 20% solution used. Which equation models this scenario?

Accepted Answer

$$0.2x + 0.5(10-x) = 3$$

Question 6

Which of the following is a solution to the equation $$x^2 + 2x + 5 = 0$?

Accepted Answer

$$x = -1 \pm 2i$$

Question 7

Solve the radical equation $$\sqrt{3x - 2} = x - 2.$$

Accepted Answer

$$x = 3$$

Question 8

Solve the compound inequality $$2 \u003c 3x - 1 \u003c 8.$$

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 9

Solve the absolute value equation $$|x + 4| = 2x.$$

Accepted Answer

$$x = -2,\ x = 4$$

Question 10

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. If a customer has $$\65$ to spend, what is the maximum number of miles they can drive?

Accepted Answer

$$200$$

Question 11

Which of the following best describes the solutions to $$x^2 + 6x + 13 = 0$?

Accepted Answer

Two complex solutions

Question 12

Solve the radical equation $$\sqrt{2x + 3} = 5.$$

Accepted Answer

$$x = 11$$

Question 13

Solve the compound inequality $$-4 \leq 5x + 1 \u003c 11.$$

Accepted Answer

$$-1 \leq x \u003c 2$$

Question 14

Solve the absolute value equation $$|3x - 7| = 2.$$

Accepted Answer

$$x = 3,\ x = \dfrac{5}{3}$$

Question 15

A biologist is studying a bacteria population that doubles every 3 hours. If the initial population is 500, how many bacteria will there be after 9 hours?

Accepted Answer

$$4000$$

Key Precalculus Equations and Problem Types: Quadratics, Radicals, Inequalities, and Absolute Value

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