Answer:
To solve the inequality |3x - 7| - 5 < -14, you can follow these steps:
1. Add 5 to both sides of the inequality to isolate the absolute value term:
|3x - 7| - 5 + 5 < -14 + 5
This simplifies to:
|3x - 7| < -9
2. Now, we need to consider two cases for the absolute value:
Case 1: 3x - 7 is positive:
3x - 7 < -9
Add 7 to both sides:
3x < -9 + 7
3x < -2
Divide by 3 (remember to reverse the inequality because you're dividing by a negative number):
x < -2/3
Case 2: 3x - 7 is negative:
-(3x - 7) < -9
Distribute the negative sign on the left side:
-3x + 7 < -9
Subtract 7 from both sides:
-3x < -9 - 7
-3x < -16
Divide by -3 (remember to reverse the inequality again):
x > 16/3
So, the solution to the inequality |3x - 7| - 5 < -14 is:
x < -2/3 or x > 16/3
These are the two separate cases for which the inequality holds true.
Explanation: