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:
The solution set of given inequality is [tex]-4\leq x\leq 2[/tex].
Step-by-step explanation:
If an absolute inequality is defined as
[tex]|x|\leq a[/tex], then [tex]-a\leq x\leq a[/tex]
The given inequality is
[tex]|3x+3|\leq 9[/tex]
This absolute inequality can be rewritten as
[tex]-9\leq 3x+3\leq 9[/tex]
By this compound inequality we get
[tex]-9\leq 3x+3[/tex]
Subtract 3 from both sides.
[tex]-9-3\leq 3x+3-3[/tex]
[tex]-12\leq 3x[/tex]
Divide both sides by 3.
[tex]-4\leq x[/tex]
[tex]3x+3\leq 9[/tex]
Subtract 3 from both sides.
[tex]3x+3-3\leq 9-3[/tex]
[tex]3x\leq 6[/tex]
Divide both sides by 3.
[tex]x\leq 2[/tex]
Therefore the solution set of given inequality is [tex]-4\leq x\leq 2[/tex].
