Expert Answers
hala718 eNotes educator| Certified Educator

Given the equation:

9 l 5x-3 l = 90

We need to solve for x.

First, we need to isolate the absolute value on the left side by itself.

Then, we will divide by 9 both sides.

==> l 5x-3 l = 10

Now we have two cases:

Case(1): (5x-3) = 10

==> 5x = 13

==> x= 13/5

Case(2): -(5x-3) = 10

==> -5x +3 = 10

==> -5x = 7

==> x = -7/5

Then, we have two answers:

x = -7/5 and x=13/5

givingiswinning | Student

9l5x-3l = 90

|5x-3|=10

5x-3=10                                                

5x=13                                              

x=13/5                      

5x-3=-10

5x=-7

x=-7/5

taangerine | Student

 Divide the 9 to the other side to isolate the absolute value. 

 l5x-3l = 10

Get rid of the absolute value

-10<5x-3<10

Add 3 to all sides

-7<5x<13

Isolate x by dividing 5 to all sides

-7/5<x<13/5

atyourservice | Student

9l5x-3l = 90

|5x-3|=10

5x-3=10                    or                            5x-3=-10

5x=13                       or                            5x=-7

x=13/5                      or                           x=-7/5

nisarg | Student

 9l5x-3l = 90

|5x-3|=10

5x-3=10        5x-3=-10

5x=13           5x=-7

x=13/5  or     x=-7/5

Wiggin42 | Student

9l5x-3l = 90

Isolate the absolute value: 

| 5x - 3 | = 10

Since its an absolute value; you have two equations: 

5x - 3 = 10      and   5x - 3 = -10

You can solve both sides separately and get that 

x = -7/5 and x = 13/5