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STatiana [176]
3 years ago
13

Solve 8 − |2x − 1| ≥ 6. State your answer in interval notation

Mathematics
1 answer:
Gnoma [55]3 years ago
3 0

Answer:

\huge\boxed{x\in[-0.5,\ 1.5]}

Step-by-step explanation:

8-|2x-1|\geq6\qquad\text{subtract 8 from both sides}\\\\8-8-|2x-1|\geq6-8\\\\-|2x-1|\geq-2\qquad\text{change the signs}\ /\text{multiply both sides by (-1)}/\\\\|2x-1|\leq2\iff2x-1\leq2\ \wedge\ 2x-1\geq-2\qquad\text{add 1 to all sides}\\\\2x-1+1\leq2+1\ \wedge\ 2x-1+1\geq-2+1\\\\2x\leq3\ \wedge\ 2x\geq-1\qquad\text{divide all sides by 2}\\\\\dfrac{2x}{2}\leq\dfrac{3}{2}\ \wedge\ \dfrac{2x}{2}\geq\dfrac{-1}{2}\\\\x\leq1.5\ \wedge\ x\geq-0.5\Rightarrow-0.5\leq x\leq1.5

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