What is x if the identity is true |2-3x|-|2x-3|=0 ?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have the identity |2-3x|-|2x-3|=0

|2-3x|-|2x-3|=0

=> |2-3x| = |2x-3|

This gives us 2 - 3x = 2x - 3

=> 5x = 5

=> x = 1

and 2 - 3x = 3 - 2x

=> x = -1

So we get x = 1 and x = -1

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll solve the equation considering 4 cases of study.

The expressions 2x-3 and 2-3x can be either positive or negative.

Case 1:

2x-3 = 2-3x

Case 2:

-(2x-3) = 2-3x

Case 3:

2x-3 = -(2-3x)

Case 4:

-(2x-3) = -(2-3x)

The Case 2 and Case 3 will have the same solution. Also Case 1 and Case 4 will have the same solution. So, we'll solve just Case 1 and Case 2:

Case 1:

2x-3 = 2-3x

We'll isolate x to the left side:

2x + 3x = 3+2

5x = 5

We'll divide by 5:

x = 1

Case 2:

-(2x-3) = 2-3x

We'll remove the brackets:

-2x +3 = 2-3x

We'll isolate x to the left side:

-2x + 3x = 2-3

x = -1

The solutions of the equation are: {-1 ; 1}.

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