1. |x| < 3
-3 < x < 3
Answer: O
2. |x| ≥ 4
x ≤ -4 or x ≥ 4
Answer: S
3. |x + 3| ≥ 6
x + 3 ≤ -6 or x + 3 ≥ 6
x ≤ -9 or x ≥ 3
Answer: I
4. |4x - 3| ≤ 11
-11 ≤ 4x - 3 ≤ 11
-8 ≤ 4x ≤ 14
-2 ≤ x ≤ 3.5
Answer: G
5. |x - 5| + 2 > 7
|x - 5| > 5
x - 5 < -5 or x - 5 > 5
x < 0 or x > 10
Answer: M
6. 3|2x - 1| < 6
|2x - 1| < 2
-2 < 2x - 1 < 2
-1 < 2x < 3
-0.5 < x < 1.5
Answer: E
7. |x| > 2
x < -2 or x > 2
Answer: M
8. |x| ≤ 5
-5 ≤ x ≤ 5
Answer: E
9. |x + 4| ≤ 7
-7 ≤ x + 4 ≤ 7
-11 ≤ x ≤ 3
Answer: G
10. |2x + 7| ≥ 15
2x + 7 ≤ -15 or 2x + 7 ≥ 15
2x ≤ -22 or 2x ≥ 8
x ≤ -11 or x ≥ 4
Answer: S
11. |x - 8| - 1 < 15
|x - 8| < 16
-16 < x - 8 < 16
-8 < x < 24
Answer: N
12. 2|3x - 4| ≥ 10
|3x - 4| ≥ 5
3x - 4 ≤ -5 or 3x - 4 ≥ 5
3x ≤ -1 or 3x ≥ 9
x ≤ -1/3 or x ≥ 3
Answer: Y
13. -3|x + 1| > -12
|x + 1| < 4
-4 < x + 1 < 4
-5 < x < 3
Answer: O
14. -|4x| + 7 < 3
-|4x| < -4
|4x| > 4
4x < -4 or 4x > 4
x < -1 or x > 1
Answer: C
The decoded quote is: "You are never too old to set another goal or to dream a new dream."
Parent Tip: Review the logic above to help your child master the concept of absolute value inequalities worksheet.
