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Answer :
The solution to the inequality -|x-9/5+13/15| ≥ 7 is x ≥ 14/15 or x < 14/15.
What is the solution of the inequality?
The solution to the inequality: -|x-9/5+13/15| ≥ 7 is solved in two ways:
- when the expression inside the absolute value is positive and
- when it is negative.
Case 1: (x-9/5+13/15) ≥ 0
x - 9/5 + 13/15 ≥ 0
x - 9/5 + 13/15 ≥ 0
15x - 27 + 13 ≥ 0
15x - 14 ≥ 0
15x ≥ 14
x ≥ 14/15
Case 2: (x-9/5+13/15) < 0
x - 9/5 + 13/15 < 0
x - 9/5 + 13/15 < 0
15x - 27 + 13 < 0
15x - 14 < 0
15x < 14
x < 14/15
Therefore, the solutions from both cases give; x ≥ 14/15 or x < 14/15
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