Question

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

Answer 1

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

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}\\\\(2x)/(2)\leq(3)/(2)\ \wedge\ (2x)/(2)\geq(-1)/(2)\\\\x\leq1.5\ \wedge\ x\geq-0.5\Rightarrow-0.5\leq x\leq1.5`