CH2 2.7 Absolute Value Inequalities

Question 1

Match the absolute value statement with its equivalent statement.

|5x+4| ≤ 9

Answer 1

-9 ≤ 5x + 4 ≤ 9

Question 2

Match the absolute value statement with its equivalent statement.

Answer 2

-12 < 8x + 4 < 12

Question 3

Match the absolute value statement with its equivalent statement.

|5x + 4| ≥ 9

Answer 3

5x + 4 ≥ 9 or 5x + 4 ≤ -9

Question 4

Match the absolute value statement with its equivalent statement.

|9x + 8|> 17

Answer 4

9x + 8 > 17 or 9x + 8 < -17

Question 5

Solve the inequality. Graph the solution set.

|x-3|< 4

Answer 5

The solution set is
(-1,7)

(Find the solution set first the graph)

Question 6

Solve the inequality. Then graph the solution set and write it in interval notation.

|2x + 6| ≤ 20

Answer 6

The solution set is
[-13, 7]

(Find the solution set first the graph)

Question 7

Solve the inequality. Then graph the solution set and write it in interval notation.

|x |+ 7≤ 9

Answer 7

The solution set is [-2, 2]

(Find the solution set first then graph)

Question 8

Solve the inequality. Then graph the solution set and write it in interval notation.
|5x − 5| < − 30

Answer 8

The solution set is

No solution

(There will be nothing to graph)

Question 9

Solve the inequality. Then graph the solution set and write it in interval notation.

|x − 8| − 8 ≤ − 1

Answer 9

The solution set is
[1,15]

(Find the solution set first then graph)

Question 10

Solve the following inequality and graph the solution set.

|x| > 9

Answer 10

The solution is an interval. The solution is

(−∞,−9) ∪ (9,∞)

(Find the solution then graph)

Question 11

Solve the following inequality and graph the solution set.
|x + 7| ≥ 18

Answer 11

The solution is an interval. The solution is
(−∞,−25] ∪ [11,∞)

(Find the solution then graph)

Question 12

Solve the following inequality and graph the solution set.

|x| + 2 > 7

Answer 12

The solution is an interval. The solution is
(−∞,−5) ∪ (5,∞)

(Find the solution the graph)

Question 13

Solve the inequality. Graph the solution set and write it in interval notation.

|3x| > − 5

Answer 13

The solution set is
(−∞,∞)

(Find the solution then graph)

Question 14

Solve the inequality |6x − 11| + 3 > 10. Graph the solution set and write it in interval notation.

Answer 14

Written in interval​ notation, the solution is
(−∞,2/3 ∪ (3,∞)

(Find the solution then graph)

Question 15

Solve the inequality. Graph the solution set.

|4x+3| > 0

Answer 15

The solution is one or more intervals. The solution is
(- ∞,3/4) ∪ (−3/4,∞)

(Find the solution then graph)

Question 16

Solve the following inequality and graph the solution set.

|2x − 5| ≤ 11

Answer 16

The solution is an interval. The solution is
[−3,8]

(Find the solution first then graph)

Question 17

Solve the following inequality and graph the solution set.

|x+1|+ 5 ≥ 9

Answer 17

The solution is an interval.
(−∞,−5] ∪ [3,∞)

(Find the solution first then graph)