Question

given rectangle uvwx below, uy = 40. if vx = -2x + 6, solve for x.

Explanation:

Step1: Recall property of rectangle diagonals

In a rectangle, the diagonals bisect each other. So \( VX = 2UY \).

Step2: Substitute values into the equation

Given \( UY = 40 \), then \( VX=2\times40 = 80 \). Also \( VX=-2x + 6 \). So \( -2x+6 = 80 \).

Step3: Solve the equation for \( x \)

Subtract \( 6 \) from both sides: \( -2x=80 - 6=74 \).
Divide both sides by \( -2 \): \( x=\frac{74}{-2}=-37 \).

Answer:

\( x=-37 \)