Answer
$(-∞,\frac{13}{5}]U[4,∞)$
Work Step by Step
We are given that $5x-3\leq10$ or $x+1\geq5$. Therefore, a solution only needs to satisfy one of the inequalities.
We can first solve $5x-3\leq10$ for x.
Add 3 to both sides.
$5x\leq13$
Divide both sides by 5.
$x\leq\frac{13}{5}$
Next, can first solve $x+1\geq5$ for x.
Subtract 1 from both sides.
$x\geq4$
Therefore, the solution set consists of all real numbers that are less than or equal to $\frac{13}{5}$ or greater than or equal to 4.
