Question

for what value of x must abcd be a parallelogram?
for abcd to be a parallelogram, the value of x must be \boxed{}. (simplify your answer)
image of quadrilateral abcd with diagonals, labeled with 4x, x, and 5x - 3

Explanation:

Step1: Recall parallelogram diagonal property

In a parallelogram, the diagonals bisect each other. So, the segments of one diagonal are equal. Here, \(4x\) and \(5x - 3\) should be equal.

$$4x=5x - 3$$

Step2: Solve for \(x\)

Subtract \(4x\) from both sides:

$$0=x - 3$$

Add 3 to both sides:

$$x = 3$$

Answer:

\(3\)