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Solve the inequality and give |3x-7|-5<-14

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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:

User Matthew Ruddy
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