Given:

2x-1-x+5=3

Calculation:

By the definition of absolute value,

2x-1=1-2x,  x<122x-1,  x≥12 and x+5=-x-5,  x<-5x+5,  x≥-5 

Solve for x by equating each expression to zero.

2x-1=0

2x=1

x=12

Similarly,

 x + 5=0

x = - 5

We obtain the three intervals in which the equation has three different forms.

I. x< -5

II. - 5≤x< 12

 III. x ≥ 12

I.

If x< -5, we have

 2x-1-x+5=3

1-2x - -x-5 =3

- x+4=3

Adding -4 on both sides

- x=3-4

x=1

But x=1 is not in the interval x< -5.

II.

2x-1-x+5=3

1-2x - x + 5 =3

1-2x-x-5=3

-3x-4=3

Adding 4 on both sides

-3x=7

x=- 73

This is the correct solution because it belongs to interval - 5≤x< 12.

III.

2x-1-x+5=3

2x-1 - x + 5 =3

2x-1-x-5=3

x-6=3

x=9

This is the correct solution because it belongs to interval x ≥ 12.

x= - 73 and x=9

Conclusion:

We were able to solve 2x-1-x+5=3, and find the value of x.