Answer:
[tex]-9 \leq x \leq 9[/tex]
Step-by-step explanation:
When solving absolute value equations, we have to remember a simple rule:
[tex]|a|<b[/tex] means
a < b
and
a < -b
Now, onto our equation:
[tex]|9x| \leq 81[/tex]
We can write:
1. [tex]9x \leq 81[/tex]
and
2. [tex]9x \leq -81[/tex]
Solving #1,
[tex]9x\leq81\\x\leq9[/tex]
Solving #2,
[tex]9x\leq -81\\x \geq -9[/tex]
Note: remember to change inequality signs when dealing with negatives
So, the solution is all numbers between -9 and 9 inclusive. Or in other words:
[tex]-9 \leq x \leq 9[/tex]
ANswer choices are wrong.
