Final answer:
The value of x is found by setting the sum of AB and CD equal to AC and solving for x, which results in x being 7.8.
Step-by-step explanation:
To find the value of x algebraically when given AC = 40, BD = 40, AB = 2x + 3, and CD = 3x - 2, we start by observing that AC and BD are diagonals of a rectangle, line segment or otherwise intersecting lines that are equal in length.
We can set AB + CD equal to AC to find x:
2x + 3 + 3x - 2 = 40
5x + 1 = 40
5x = 39
x = 39/5
x = 7.8
Therefore, the value of x is 7.8.