Question

for what value of x must abcd be a parallelogram?
for abcd to be a parallelogram, the value of x must be \square. (simplify your answer.)

Explanation:

Step1: Recall parallelogram diagonal property

In a parallelogram, the diagonals bisect each other. So the segments of one diagonal are equal. Here, the sides related to \(x\) should be equal, so \(2x = 3x - 9\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(0 = 3x - 2x - 9\), which simplifies to \(0 = x - 9\). Then add 9 to both sides: \(x = 9\).

Answer:

\(9\)