If ABCD is a rectangle with center Z (where the diagonals bisect), and AC = 3x+11 and BD = 2x+31, what is x?

since the diagonals are equal,

3x+11 = 2x+31
x = 20

To find the value of x, we can set the lengths of the diagonals equal to each other:

AC = BD

Substituting the given expressions for AC and BD:

3x + 11 = 2x + 31

Simplifying the equation:

3x - 2x = 31 - 11

x = 20

Therefore, x is equal to 20.

To find the value of x, we can use the property of rectangles that states the diagonals are congruent and bisect each other.

Since ABCD is a rectangle, the diagonals AC and BD are equal in length. Therefore, we can set the expressions for AC and BD to be equal and solve for x:

AC = BD
3x + 11 = 2x + 31

To solve this equation, we can aim to isolate the variable x by moving all terms containing x to one side of the equation:

3x - 2x = 31 - 11
x = 20

Therefore, x = 20.