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Solve the absolute value inequality. -3|4-x|<-15

User Pedryk
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Final answer:

The solution to the inequality -3|4-x| < -15 is x < -1 or x > 9, after considering the cases for the absolute value and reversing the inequality sign upon dividing by a negative number.

Step-by-step explanation:

The inequality in question is -3|4-x| < -15. First, we divide both sides of the inequality by -3, remembering that this will reverse the inequality sign since -3 is negative. This yields |4-x| > 5. Now, we solve for the absolute value inequality which means we have to consider two cases.

Case 1 (positive): 4-x > 5

1. Subtract 4 from both sides: -x > 1

2. Multiply both sides by -1 (inequality sign flips): x < -1

Case 2 (negative): 4-x < -5

1. Subtract 4 from both sides: -x < -9

2. Multiply both sides by -1 (inequality sign flips): x > 9

The solution to the inequality is therefore x < -1 or x > 9.

User Seoyoochan
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