A trapezoid has base lengths of (6x-1) units and 3 units. Its midsegment has a length of (5x-3) units. What is the value of x?

1. You have that:

- The lengths of the bases are (6x-1) units and 3 units.

- The midsegment has a length of (5x-3) units.

2. To solve this exercise, you must apply the formula for calculate the length of the midsegment of a trapezoid, which is shown below:

Midsegment=Base1+Base2/2

As you can see, the midsegment is half the sum of the bases of the trapezoid.

3. When you substitute the values, you obtain:

(5x-3) = [ (6x-1) + 3]/2

4. Now, you can solve the problem by clearing the "x":

(5x-3) = [ (6x-1) + 3]/2

2 (5x-3) = 6x-1+3

10x-6=6x+2

10x-6x=2+6

4x=8

x=8/4

x=2