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

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hala718 eNotes educator | Certified Educator

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

We have two cases:

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

==> We will combine like terms.

==> -2x -2x = -5 -5

==> -4x = -10

Divide by -4.

==> x = 10/4 = 5/2= 2.5...........(1)

Case (2):

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

==> 2x -5 = 2x -5

==> 0 = 0

==> the answer is all x values such that - (-2x+5) > 0

==> 2x -5 >0

==> 2x > 5

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

Then, from (1) and (2) we have:

x=  [ 5/2, inf)

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justaguide eNotes educator | Certified Educator

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We have to solve the equation |-2x + 5| = 2x - 5

Now |-2x + 5| = -2x + 5 or 2x - 5

So we get -2x + 5 = 2x - 5

=> 4x = 10

=> x= 5/2

and 2x - 5 = 2x - 5, which does not yield a solution

The required value of x is 5/2

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