Question

I need to solve the absolute value inequality and write interval notation for the solution set?

Answer 1

Given:

The inequality is,

`|2x-6|\leq14`

Simplify the inequality,

`\begin{gathered} |2x-6|\leq14 \\ \textApply the absolute rule, If \leq u\text{ Then -u}\leq a\leq u \\ -14\leq(2x-6)\leq14 \\ -14+6\leq2x\leq14+6 \\ -8\leq2x\leq20 \\ -(8)/(2)\leq x\leq(20)/(2) \\ -4\leq x\leq10 \end{gathered}`

Answer: The solution set is [-4,10].