Question 1

Which of the following is the correct solution to the equation $$2x - 3 = 7$$?

Accepted Answer

$$x = 5$$

Question 2

If $$|x - 4| = 7$$, what are the possible values of $$x$$?

Accepted Answer

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

Question 3

Solve the inequality $$3x + 2 \u003c 11$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, 3)$$

Question 4

Which of the following is the correct solution to $$|2x + 1| = 5$$?

Accepted Answer

$$x = 2 or$$ $$x = -3$$

Question 5

What is the solution to the compound inequality $$-2 \u003c x + 3 \leq 5$$?

Accepted Answer

$$(-5, 2]$$

Question 6

If $$|x| \u003c 4$$, what is the solution set in interval notation?

Accepted Answer

$$(-4, 4)$$

Question 7

Solve the absolute value inequality $$|x - 2| \geq 5$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, -3] \cup [7, \infty)$$

Question 8

Which of the following is a correct step when solving $$|3x - 4| = 8$$?

Accepted Answer

Set $$3x - 4 = 8$$ and $$3x - 4 = -8$$

Question 9

What is the solution to $$|x + 1| \u003c 3$$?

Accepted Answer

$$(-4, 2)$$

Question 10

If you multiply both sides of an inequality by a negative number, what must you do?

Accepted Answer

Reverse the direction of the inequality symbol

Question 11

Solve the equation $$\frac{2x - 4}{3} = 6.$$

Accepted Answer

$$x = 7$$

Question 12

Which interval represents the solution to $$|x| \geq 2$$?

Accepted Answer

$$(-\infty, -2] \cup [2, \infty)$$

Question 13

What is the solution to $$|2x + 3| \u003c 7$$?

Accepted Answer

$$(-5, 2)$$

Question 14

Which of the following is a correct way to solve $$|x - 5| = 0$$?

Accepted Answer

Set $$x - 5 = 0$$

Question 15

If $$|x + 2| \u003e 6$$, what is the solution set in interval notation?

Accepted Answer

$$(-\infty, -8) \cup (4, \infty)$$

Question 16

Which of the following is the correct solution to the compound inequality $$-3 \u003c x \u003c 5$$?

Accepted Answer

$$(-3, 5)$$

Question 17

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

Accepted Answer

No solution

Question 18

Which of the following is the correct solution to $$|x - 3| \leq 0$$?

Accepted Answer

$$x = 3$$

Question 19

If $$|x + 1| \leq 4$$, what is the solution set in interval notation?

Accepted Answer

$$[-5, 3]$$

Question 20

Which of the following is the correct solution to $$|2x - 1| \u003e 7$$?

Accepted Answer

$$(-\infty, -3) \cup (4, \infty)$$

Linear and Absolute Value Equations and Inequalities: Precalculus Study Notes

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