Question

Solve the following inequality algebraically. 5 |x – 5| – 8 =< 47

Answer 1

The inequality is:

`5\lvert x-5\rvert-8\le47`

firs we add 8 in bouth sides of the inequation so:

`\begin{gathered} 5\lvert x-5\rvert\le47+8 \\ 5\lvert x-5\rvert\le55 \end{gathered}`

Now we divide by 5 so:

`\begin{gathered} \lvert x-5\rvert\le(55)/(5) \\ \lvert x-5\rvert\le11 \end{gathered}`

now we break the absolute value by addig the maximun

`-11\le x-5\le11`

and finally we add 5 so:

`\begin{gathered} -11+5\le x\le11+5 \\ -6\le x\le16 \end{gathered}`