l x-3 l = l 2x+5 l find x values

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l x-3 l = l 2x+5 l

We have 4 cases:

case (1):

x-3 = 2x+ 5

==> -x = 8

==> x= -8

Case(2)

-(x-3) = 2x+ 5

-x + 3 = 2x + 5

-3x = 2

==> x= -2/3

Case(3):

(x-3) = -(2x+5)

x-3 = -2x - 5

3x = -2

==> x= -2/3

Case (4):

-(x-3) = -(2x+5)

-x + 3 = -2x - 5

x = -8

**==> x= { -2/3, -8}**

We are given l x-3 l = l 2x+5 l.

Now l x-3 l is equal to (x-3) if (x-3) is greater than or equal to 0 and is equal to -(x-3) if (x-3) is less than 0.

Similarly l 2x+5 l is equal to (2x+5) if (2x+5) is positive or is equal to -(2x+5) if (2x+5) is negative.

Now if x-3 < 0

=> x < 3

=> 2x + 5 can be positive or negative.

Therefore -( x-3 ) = 2x + 5

=> 3 - x = 2x + 5

=> 3x = -2

=> x = -2/3

or -(x - 3) = -2x - 5

=> 3-x = -2x - 5

=> x = -8

Now if x -3 > 0

=> x > 3

=> 2x +5 > 0

Therefore (x-3) = (2x+5)

=> x = -8

**Therefore the possible values of x are -2/3 and -8**

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