Question

find the value of the variable in the parallelogram.
$rz=3x+6$
$sw=7x-17$
$x=\square$ (simplify your answer.)

Explanation:

Step1: Recall parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $RZ = \frac{1}{2}SW$, or $2RZ = SW$.

Step2: Substitute given expressions

Substitute $RZ=3x+6$ and $SW=7x-17$ into $2RZ = SW$:
$2(3x + 6) = 7x - 17$

Step3: Expand left side of equation

$6x + 12 = 7x - 17$

Step4: Isolate x variable

Subtract $6x$ from both sides, then add 17 to both sides:
$12 + 17 = 7x - 6x$

Step5: Calculate final value of x

$29 = x$

Answer:

$29$