Question

$|x-3|\le 5$
Which of the following inequalities is equivalent to the absolute value inequality above?

• A. $-2\le x\le 8$
• B. $-8\le x\le 8$
• C. $x\le -2$ or $x\ge 8$
• D. $x\le -8$ or $x\ge 2$

Answer 1

The correct option is A $-2\le x\le 8$

Rule is when $|y|<a$

$\Rightarrow -a<y<a$

Now when $|x-3|\le 5$, then

$-7<2x-3\le 5$

Adding 3 and then dividing on both sides, we get

$-5+3\le x\le 5+3$

$-2<x<8$

Option $1.$