Question

Solve: 5|4x+5|−2≤33 Give your answer as an interval. If no solutions exists - enter No solutions.

Answer 1

The expression given is,

`5|x-3|+3>7`

Subtract 3 from both sides

`\begin{gathered} 5|x-3|+3-3>7-3 \\ 5|x-3|>4 \end{gathered}`

Divide both sides by 5

`\begin{gathered} (5|x-3|)/(5)>(4)/(5) \\ |x-3|>(4)/(5) \end{gathered}`

Apply absolute rule:

`\begin{gathered} x-3<-(4)/(5)\text{ or x-3>}(4)/(5) \\ \end{gathered}`

Add 3 to both sides

`\begin{gathered} x-3+3<-(4)/(5)+3\text{ or x-3+3>}(4)/(5)+3 \\ x<(11)/(5)\text{ or x>}(19)/(5) \end{gathered}`

Therefore, the answer has the form:

`(-\infty,A)\cup(B,\infty)`

Hence, the solution using interval notation is

`(-\infty,(11)/(5))\cup((19)/(5),\infty)`