# What are all real solutions of the equation |2x-5|=8?

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The solutions of |2x-5|=8 have to be determined.

For any number x, |x| = x if x >= 0 and |x| = -x for x < 0

Let 2x - 5 >= 0

x >= 5/2

2x - 5 = 8

2x = 13

x = 13/2 which is greater than 5/2

If 2x - 5 < 0 or x < 5/2

5 - 2x = 8

2x = -3

x = -3/2

This again is less than 5/2

The solution of |2x-5|=8 is x = -3/2 and x = 13/2

|2x-5| = 8

Since there's an absolute value signs your equation should look like

** 2x - 5 = 8 and 2x - 5 = -8 **now add 5 to both sides of both equation

By adding, your equation should look like

**2x = 13 and 2x = -3 **now divide both sides by 2 on both equation

By dividing, you should get

**x = 13/2 and x = -3/2 **

So your answers are **x = -3/2 ; 13/2 **

So there are **2 solutions to this problem **

We'll apply the property of absolute value and we'll discuss 2 cases:

2x-5 for 2x-5>=0

2x>=5

x>=5/2

-2x + 5 for 2x-5<0

2x<5

x<5/2

Case 1: x belongs to the interval [5/2, +infinite).

2x - 5 = 8

2x = 8+5

2x = 13

x = 13/2

Since x = 13/2 belongs to the interval [5/2, +infinite), we'll accept it as solution.

Case 2: x belongs to the interval (infinite,5/2).

-2x + 5 = 8

-2x = 8 - 5

-2x = 3

x = -3/2

Since x = -3/2 belongs to the interval (infinite,5/2), we'll accept it as solution.

**All real solutions of the given equation are: {-3/2 ; 13/2}.**