# x equationWhat is x if |2x-5| = 9 ?

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The absolute value |x| is the same for both x as well as -x.

|2x-5| = 9

gives two equations: 2x - 5 = 9 and 2x - 5 = -9

2x - 5 = 9

=> 2x = 14

=> x = 7

2x - 5 = -9

=> 2x = -4

=> x = -2

**The solutions of the equation are x = -2 and x = 7**

You have to do this as two separate equations because of the absolute value. They are

2x - 5 = 9

and

-2x + 5 = 9 because -(2x - 5) is -2x + 5

So now you solve each of these:

2x - 5 = 9

2x = 14

**x = 7**

-2x + 5 = 9

-2x = 4

**x = -2**

**So x = -2,7**

We recall that the absolute value means:

|p| = a>0

We'll have to solve 2 cases:

1) 2x-5 = 9

We'll add 5 both sides:

2x = 9 + 5

2x = 14

We'll divide by 2:

x = 7

2) 2x-5 = -9

We'll add 5 both sides, to isolate x to the left side:

2x = 5 - 9

2x = -4

We'll divide by 2:

x = -2

**The equation has 2 solutions : {-2 ; 7}.**