Question

given that abcd is a rectangle. bo = 3x + 32 and ac = -8x + 8, which of the following is the value of x? (1 point)

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(AC = 2AO=2BO\). Given \(BO = 3x + 32\) and \(AC=-8x + 8\), we have the equation \(-8x + 8=2(3x + 32)\).

Step2: Expand the right - hand side of the equation

Expand \(2(3x + 32)\) using the distributive property \(a(b + c)=ab+ac\). So \(2(3x + 32)=6x + 64\). The equation becomes \(-8x + 8=6x + 64\).

Step3: Move the \(x\) terms to one side and constants to the other side

Add \(8x\) to both sides: \(-8x+8x + 8=6x+8x + 64\), which simplifies to \(8 = 14x+64\). Then subtract \(64\) from both sides: \(8-64=14x+64 - 64\). So \(-56 = 14x\).

Step4: Solve for \(x\)

Divide both sides of the equation \(-56 = 14x\) by \(14\). We get \(x=\frac{-56}{14}=-4\).

Answer:

\(x = - 4\)