Answer
$[-2,\frac{8}{5}]$
Work Step by Step
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 $\frac{8}{5}$