# Solve the equation: |5x - 2| - 2 = 6

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### 8 Answers

We have to solve |5x - 2| - 2 = 6

|5x - 2| - 2 = 6

=> |5x - 2| = 8

=> 5x - 2 = 8 and 5x - 2 = -8

=> 5x = 10 and 5x = -6

=> x = 2 and x = -6/5

**The required values of x are 2 and -6/5**

l 5x -2 l -2 = 6

First we will isolate the absolute value on one side.

We will add 2 to both sides.

==> l 5x -2 l = 8

Now we have 2 cases:

Case(1):

==> (5x-2) = 8 ==> 5x = 10 ==> x = 2

Case(2):

==> -(5x-2) = 8 ==> -5x +2 = 8 ==> -5x = 6 ==> x = -6/5

**Then the answer is : x = { 2, -6/5}**

|5x - 2| - 2 = 6

5x - 2 = 8

5x = 10

x = 2

5x - 2 = -8

5x = -6

x = -6/5

|5x - 2| - 2 = 6

5x-2=8 5x=10 x=2

5x-2=-8 5x=-6 x=-6/5

|5x - 2| - 2 = 6

Since there is an absolute bar your should know that there should be 2 answers

First add 2 on both sides

By adding, your equation should look like

**|5x - 2| = 8 **since there's an absolute value sign, change your equation to

**5x - 2 = -8 and 5x - 2 = 8 **now add 2 on both sides of both equation

By adding, your equation should look like

**5x = -6 and 5x = 10 **now divide both sides of both equation by 5

By dividing it should look like

**x = -6/5 and x = 2 **which are your answers

|5x - 2| - 2 = 6

take away the 2:

5x - 2 = 8

now add 2 to both sides:

5x = 10

divide by 5

**x = 2**

since this is an absolute value problem you also need to do:

5x - 2 = -8

Complete the same steps:

5x = -6

**x = -6/5**

|5x - 2| - 2 = 6

Isolate the absolute value

|5x - 2| = 6 + 2 = 8

This is how you solve for absolute value problems:

5x - 2 = 8 AND 5x - 2 = -8

x = 2 x = -6/5

|5x - 2| - 2 = 6

We'll add 2:

|5x - 2| = 8

We'll have 2 possibilities:

5x - 2 = -8

5x = -8+2

5x = -6

x = -6/5

5x-2<0

x<2/5

Since x = -6/5 belongs to the interval of admissible solutions, we'll accept it as solution of the equation.

The second possibility:

5x - 2 = 8

5x = 10

x = 2, for x>2/5

Since x =2 belongs to the interval of admissible solutions, we'll accept it as solution of the equation.

**The solutions of the equation are: {-6/5 ; 2}.**