How do you solve abs(x-1)<=9?

Sep 9, 2016

Solution is $- 8 \le x \le 10$

Explanation:

$| x - 1 | \le 9$ means either $x - 1 \le 9$ or $- \left(x - 1\right) \le 9$

$x - 1 \le 9$

$\Leftrightarrow x \le 9 + 1$ or $x \le 10$

$- \left(x - 1\right) \le 9$

$\Leftrightarrow - x + 1 \le 9$ or $1 - 9 \le x$ or $- 8 \le x$

Hence, solution is $- 8 \le x \le 10$