Intermediate Algebra (6th Edition)

$(-∞,\frac{13}{5}]U[4,∞)$
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.