How do you solve abs(2x-9)<=11?

1 Answer
Apr 17, 2018

x<= 10 and x>=-1

Explanation:

|2x - 9| <= 11

We need to start by solving the absolute value

We know either 2x - 9 <=11 and 2x - 9 >=-11

Now we can solve the first one:

2x - 9 <= 11

Add 9 on both sides

2x - 9 + 9 <= 11 + 9

2x <= 20

Divide both sides by 2

(cancel2x)/cancel2 <= 20/2

x<=10

Now we can solve the second one

2x - 9 >= -11

Add 9 on both sides

2x - 9 + 9 >= -11 + 9

2x >= -2

Then divide both sides by 2

(2x)/2 >= (-2)/2

x >=-1

Thus,

The answers are:

x <=10 and x>=-1