Question

Solve the following inequality algebraically. -2|5 + 2x| – 6 =< -20

Answer 1

`\begin{gathered} -2|5+2x|-6\le-20 \\ |x|=x,x\ge0 \\ |x|=-x,x<0 \\ for_{\text{ }}x\ge0 \\ -2(5+2x)-6\le-20 \\ -10-4x-6\le-20 \\ -4x\le-4 \\ x\ge(-4)/(-4) \\ x\ge1 \\ \end{gathered}`
`\begin{gathered} for_{\text{ }}x<0 \\ -2(-5-2x)-6\le-20 \\ 10+4x-6\le-20 \\ 4x\le-20-4 \\ 4x\le-24 \\ x\le-(24)/(4) \\ x\le-6 \end{gathered}`

Therefore, the solutions are:

`\begin{gathered} x\ge1 \\ or \\ x\le-6 \end{gathered}`