Question

What is the solution set for this inequality? |3x+3|≤9 Graph the solution set on the number line.

Answer 1

Answer:

Step-by-step explanation:

because it's an absolute value inequality, there are two inequalities to solve

3x+3 ≤ 9 and 3x+3 ≥ -9, now we solve them separately

x ≤  3 and x ≥ -4, which is -4 ≤ x ≤ 3

Answer 2

Answer:

The solution set of given inequality is $-4\leq x\leq 2$.

Step-by-step explanation:

If an absolute inequality is defined as

$|x|\leq a$, then $-a\leq x\leq a$

The given inequality is

$|3x+3|\leq 9$

This absolute inequality can be rewritten as

$-9\leq 3x+3\leq 9$

By this compound inequality we get

$-9\leq 3x+3$

Subtract 3 from both sides.

$-9-3\leq 3x+3-3$

$-12\leq 3x$

Divide both sides by 3.

$-4\leq x$

$3x+3\leq 9$

Subtract 3 from both sides.

$3x+3-3\leq 9-3$

$3x\leq 6$

Divide both sides by 3.

$x\leq 2$

Therefore the solution set of given inequality is $-4\leq x\leq 2$.