Question

Solve |4x – 5| = 9. Show each step of your work.

Answer 1

4x - 5 = 9

4x = 14

x= 14/4

the answer is x=14/4

the equation can be checked by filling in the equation 4(14/4) - 5 + 9
14-5= 9

Answer 2

|4x-5|=9
4x-5=±9
Add 5 to each side
4x-5+5=-9+5
4x=-4
Divided 4 to each side
4x/4=-4/4
x=-1
Or
4x-5=±9
Add 5 to each side
4x-5+5=9+5
4x=14
Divided 4 to each side
4x/4=14/4
x=3.5
Check:
|4x-5|=9
Substitute x with -1
|4(-1)-5|=9
|-4-5|=9
|-9|=9
9=9
Or
|4x-5|=9
Substitute x with 3.5
|4(3.5)-5|=9
|14-5|=9
|9|=9
9=9. As a result, x=-1 and x=3.5 are both correct answers. Hope it help!