Question

Solve the absolute value inequality and write the notation for the solution set

Answer 1

`x\ge1\text{ or }x\le-4(1)/(5)`

Step-by-step explanation:

Given the absolute inequality:

`|8+5x|\ge13`

Solving the absolute inequality:

`5x+8\ge13\text{ or }5x+8\le-13`

We solve each of the inequality for x:

`\begin{gathered} 5x+8\ge13\text{ or }5x+8\le-13 \\ 5x\ge13-8\text{ or }5x\le-13-8 \\ 5x\ge5\text{ or }5x\le-21 \\ (5x)/(5)\ge(5)/(5)\text{ or }(5x)/(5)\le-(21)/(5) \\ \implies x\ge1\text{ or }x\le-4(1)/(5) \end{gathered}`

The solution to the absolute inequality are:

`x\ge1\text{ or }x\le-4(1)/(5)`

The solution set is given below:

`(-\infty,-4(1)/(5)\rbrack\cup\lbrack1,\infty)`