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iren [92.7K]
3 years ago
14

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

Mathematics
2 answers:
soldi70 [24.7K]3 years ago
8 0

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

Paladinen [302]3 years ago
8 0

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.

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