What are the values of x in the equation |-5x-2|=12?

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samhouston's profile pic

samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted on

Since this is an absolute value equation, there are two solutions:  one that produces the given value and one that produces the opposite of the given value.

-5x - 2 = 12

-5x = 14

x = -2.8

 

-5x - 2 = -12

-5x = -10

x = 2

 

You can also answer this question graphically. 

Graph:  y = abs(-5x - 2)

Graph:  y = 12

Find the two points of intersection.  The x-values of these points are the two solutions to the equation.

 

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the values of x that satisfy: |-5x-2|=12

|-5x-2|=12

=> -5x - 2 = 12 and -5x - 2 = -12

=> -5x = 14 and -5x = -10

=> x = -14/5 and x = 2

The solution of the equation is x = -14/5 and x = 2

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Applying the module property, we'll have to solve two cases:

1) -5x-2=12

-5x = 12 + 2

-5x = 14

x = -14/5

-5x - 2 > 0 => -5x > 2 => x < -2/5

Since -14/5 < -2/5, the value of x is accepted as solution of equation.

2) -5x-2=-12

-5x = -12+2

-5x = -10

x = 2

-5x-2 `<=` 0

x `>=` -2/5

Since 2 > -2/5, the value of x is accepted as solution of equation.

The requested solutions of the equation are: {-14/5 ; 2}.

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