Question

Solve |9x | ≦ 81

Select the appropriate response
A) x ≦ −82
B) x ≦ −10
C) x ≦ −9
D) x ≦ −2

Help please!

Answer 1

`-9 \leq x \leq 9`

Explanation:

When solving absolute value equations, we have to remember a simple rule:

`|a|<b` means

a < b

and

a < -b

Now, onto our equation:

`|9x| \leq 81`

We can write:

1.
`9x \leq 81`

and

2.
`9x \leq -81`

Solving #1,

`9x\leq81\\x\leq9`

Solving #2,

`9x\leq -81\\x \geq -9`

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:

`-9 \leq x \leq 9`

ANswer choices are wrong.