Answer
The solution is $(-\infty,\infty)$
Work Step by Step
$5(x-1)\ge-5$ 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
$(-\infty,\infty)$