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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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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}

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givingiswinning | Student, Grade 10 | (Level 1) Valedictorian

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|5x - 2| - 2 = 6

5x - 2 = 8

5x = 10

x = 2

5x - 2 = -8

5x = -6

x = -6/5

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nisarg | Student, Grade 11 | (Level 1) Valedictorian

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|5x - 2| - 2 = 6

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

5x-2=-8         5x=-6      x=-6/5

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jess1999 | Student, Grade 9 | (Level 1) Valedictorian

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 |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

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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|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

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Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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|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 

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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|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}.

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