Find the value of x that makes the quadrilateral a parallelogram

The value of x that makes the quadrilateral a parallelogram is:

x = 4

Step-by-step explanation:

The given quadrilateral would be a Parallelogram if the opposite sides of this quadrilateral are congruent.

As 3x + 2 and 5x - 6 are the opposite sides, so

5x - 6 = 3x + 2

subtracting 3x from both sides

5x - 6 - 3x = 3x + 2 - 3x

2x - 6 = 2

adding 6 to both sides

2x - 6 + 6 = 2 + 6

2x = 8

divide both sides by 2

2x/2 = 8/2

x = 4

Therefore, the value of x that makes the quadrilateral a parallelogram is:

x = 4

Verification:

5x - 6 = 5(4) - 6 = 20 - 6 = 14

3x + 2 = 3(4) + 2 = 12 + 2 = 14