## Intermediate Algebra (6th Edition)

The solution is $(-\infty,\infty)$
$5(x-1)\ge-5$ or $5+x\le11$ Solve the first inequality. $5(x-1)\ge-5$ Evaluate the product on the left side: $5x-5\ge-5$ Take $5$ to the right side: $5x\ge-5+5$ $5x\ge0$ Take $5$ to divide the right side: $x\ge\dfrac{0}{5}$ $x\ge0$ Expressing in interval notation: $[0,\infty)$ Solve the second inequality: $5+x\le11$ Take $5$ to the right side: $x\le11-5$ $x\le6$ Expressing the solution in interval notation: $(-\infty,6]$ Since the compound inequality is formed by the word "or", the solution is formed by the solution of both inequalities: $(-\infty,6]\cup[0,\infty)$ or $(-\infty,\infty)$