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Math

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PROBLEM

Week 15 - Inequalities
Questi
Solve the inequality.
5x+8+9<2|5 x+8|+9<2

STEP 1

1. The inequality involves an absolute value expression.
2. We will need to isolate the absolute value term and split the inequality into two separate inequalities to solve it.

STEP 2

1. Isolate the absolute value expression 5x+8 |5x + 8| .
2. Split the absolute value inequality into two separate inequalities.
3. Solve each inequality.
4. Combine the solutions.

STEP 3

First, subtract 9 from both sides of the inequality to isolate the absolute value expression:
5x+8+9<2 |5x + 8| + 9 < 2 5x+8<29 |5x + 8| < 2 - 9 5x+8<7 |5x + 8| < -7

SOLUTION

Recognize that an absolute value expression is always non-negative, meaning 5x+80 |5x + 8| \geq 0 . Therefore, it can never be less than a negative number.
Since 5x+8<7 |5x + 8| < -7 is impossible (as absolute values cannot be negative), there are no solutions to this inequality.
The solution to the inequality is:
No solutions exist.

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