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:

\(3\)