Question

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

Answer 1

Answer:

$x\ge1\text{ or }x\le-4\frac{1}{5}$

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:

$\begin{gathered} 5x+8\ge13\text{ or }5x+8\le-13 \\ 5x\ge13-8\text{ or }5x\le-13-8 \\ 5x\ge5\text{ or }5x\le-21 \\ \frac{5x}{5}\ge\frac{5}{5}\text{ or }\frac{5x}{5}\le-\frac{21}{5} \\ \implies x\ge1\text{ or }x\le-4\frac{1}{5} \end{gathered}$

The solution to the absolute inequality are:

$x\ge1\text{ or }x\le-4\frac{1}{5}$

The solution set is given below:

$(-\infty,-4\frac{1}{5}\rbrack\cup\lbrack1,\infty)$