## Intermediate Algebra (6th Edition)

$[-2,\frac{8}{5}]$
We are given that $|5x+1|+1\leq10$. First, subtract 1 from both sides. $|5x+1|\leq9$ Therefore, $5x+1\leq9$ and $5x+1\geq-9$. We can solve these equations for x to find solutions. For $5x+1\leq9$, subtract 1 from both sides. $5x\leq8$ Divide both sides by 5. $x\leq\frac{8}{5}$ For $5x+1\geq-9$, subtract 1 from both sides. $5x\geq-10$ Divide both sides by 5. $x\geq-2$ So the absolute-value inequality is satisfied for all values of x that are greater than or equal to -2 and less than or equal to $\frac{8}{5}$