We have the equation |2x – 3| = 7 which we have to solve for x.

Now |2x – 3| = 2x – 3 for 2x – 3 > 0

and is equal to (3 - 2x) for 2x – 3 < 0

Let’s assume 2x – 3 > 0

=> 2x – 3 =7

=> 2x = 10

=> x = 10/2

=> x = 5

If we assume that 2x – 3< 0

=> 3 – 2x = 7

=> -2x = 4

=> x = 4/-2

=> x = -2

**Therefore the equation has two solutions x= 5 and x = -2.**

To solve the equation |2x-3| = 7.

|2x-3| implies 2x-3 if 2x-3 >0.

|2x-3| implies 3-2x , if 2x-3 < 0.

So we solve the equations for the two cases.

When 2x-3> 0, Or x > 3/2.

2x-3 = 7. Or 2x= 7+3. Or 2x = 10. Or x = 10/2 = 5.

cas2:

When 2x-3<0, x < 3/2.

3-2x = 7. Or 3-7 = 2x. Or -4 = 2x. Or - 4/2 = x. Or x =-2.

Therefore x = 5 or x = -2 are the solutions.

We'll solve the equations considering 2 cases:

2x-3 for 2x-3>=0

2x>=3

x>=3/2

-2x + 3 for 2x-3<0

2x<3

x<3/2

Case 1: x belongs to the interval [3/2, +infinite).

2x - 3 = 7

2x = 10

**x = 5**

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

Case 2: x belongs to the interval (infinite,3/2).

-2x + 3 = 7

-2x = 4

**x = -2**

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