Solve for x if l 2x-3 l = l x-2 l

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to solve for x given that | 2x - 3| = |x - 2|

2x - 3 and 3 - 2x give the same value for |2x - 3| and 2 - x and x - 2 give the same value for |x - 2|

So we have:

2x - 3 = x - 2

=> x = 1

2x - 3 = 2 - x

=> x = 5/3

3 - 2x = x - 2

=> x = 5/3

3 - 2x = 2 - x

=> x = 1

The required solution is x = 1 and x = 5/3

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

Posted on

Given the equation of absolute values:

l 2x-3 l = l x-2 l

We need to find the values of x that verifies the equation.

We have 4 cases:

case(1):

2x-3 = x-2

==> x = 1 .......(1)

case(2) :

-(2x-3) = x-2

-2x +3 = x-2

==> -3x = -5

==> x= 5/3 .............(2)

Case(2):

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

-2x+3 = -x +2

==> -x = -1

==> x= 1...............(3)

Case(4) :

2x-3 = -(x-2)

2x-3 = -x + 2

==> 3x = 5

==> x= 5/3.............(4)

From the above cases we conclude that the solution is:

x= { 5/3 , 1}

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