Answer in fraction form: -17/4 < x < 11/4
Answer in decimal form: -4.25 < x < 2.75
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Work Shown:
|4x+3| - 9 < 5
|4x+3| < 5+9 .... adding 9 to both sides
|4x+3| < 14
-14 < 4x+3 < 14 .... see note at the bottom
-14-3 < 4x < 14-3 .... subtracting 3 from all sides
-17 < 4x < 11
-17/4 < x < 11/4 .... divide all sides by 4
-4.25 < x < 2.75
This says that x is between -4.25 and 2.75, but x is not equal to either endpoint.
Note: I used the rule that |x| < k becomes -k < x < k where k is a positive real number.