Question

Solve the following inequality algebraically. 2|3 – 3x| - 8 =>10

Answer 1

We have the following:

`2|3-3x|-8\ge10​`

solving for x

`\begin{gathered} 2|3-3x|-8\ge10​ \\ 2|3-3x|-8+8\ge10​+8 \\ (2)/(2)|3-3x|\ge(18)/(2) \\ |3-3x|\ge9 \\ 3-3x\ge9\rightarrow-3x\ge6\rightarrow x\leq(6)/(-3)\rightarrow x\leq-2 \\ 3-3x\leq-9\rightarrow-3x\leq-12\rightarrow x\ge(-12)/(-3)\rightarrow x\ge4 \end{gathered}`

The answer is:

`(-\infty,-2\rbrack\cup\lbrack4,\infty)`