Question 1

Solve the absolute value inequality $$|7x - 7| \u003c 28$$ and express the solution in interval notation.

Accepted Answer

$$( -3, 5 )$$

Question 2

Solve and check the linear equation: $$9x - (7x - 4) = 12.$$

Accepted Answer

$$x = 2$$

Question 3

Solve the radical equation $$\sqrt{3 - 2x} = x$$ and check for extraneous solutions.

Accepted Answer

$$x = 1$$

Question 4

Divide and express in standard form: $$\dfrac{4i}{3 - 9i}.$$

Accepted Answer

$$-\dfrac{2}{15} + \dfrac{2}{15}i$$

Question 5

After a 90% reduction, you purchase a washing machine on sale for $76. What was the original price?

Accepted Answer

$$760$$

Question 6

Solve using the square root property: $$(x - 8)^2$ = 49.$$

Accepted Answer

$$x = 1 or$$ $$x = 15$$

Question 7

Solve the linear inequality $$3(7 - 2x) \geq 19 - 4x$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 2]$$

Question 8

Solve the quadratic equation by factoring: $$x^2 = 3x + 10$.

Accepted Answer

$$x = -2, x = 5$$

Question 9

A person will devote 34 years total to sleeping and watching TV over a lifetime. The years spent sleeping exceed the years spent watching TV by 18. How many years will the person spend on each activity?

Accepted Answer

Sleeping: 26 years, TV: 8 years

Question 10

Solve the compound inequality $$-7 + 2x + 1 \leq -1$$ and express your answer in interval notation.

Accepted Answer

$$x \leq 3$$

Question 11

Solve using the quadratic formula: $$5x^2 + 4x + 2 = 0$.

Accepted Answer

$$x = \dfrac{-4 \pm \sqrt{16 - 40}}{10}$$

Question 12

Which of the following best describes the solution set for $$|x - 3| \u003e 5$$?

Accepted Answer

$$( -\infty, -2 ) \cup (8, \infty )$$

Question 13

If $$x is a $$real number, which of the following is always true for $$|x| \leq 7$$?

Accepted Answer

$$-7 \leq x \leq 7$$

Question 14

Which of the following is the correct solution to $$2(x - 3) = 4x + 8$$?

Accepted Answer

$$x = -7$$

Question 15

A chemist needs to mix a solution that is 30% acid with one that is 10% acid to obtain 20 liters of a 20% acid solution. How many liters of the 30% solution should be used?

Accepted Answer

10 liters

Chapter 1 Test Review: Equations and Inequalities (Precalculus Guidance)

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