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) x = 28 x = -24/11 x = -16/19 x = -4

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal and bisect each other. So $AC = 2BO$.

Step2: Substitute expressions

Substitute $BO = 3x + 32$ and $AC=-8x + 8$ into $AC = 2BO$. We get $-8x + 8=2(3x + 32)$.

Step3: Expand right - hand side

Expand $2(3x + 32)$ to get $6x+64$. So the equation is $-8x + 8=6x+64$.

Step4: Move x terms to one side

Add $8x$ to both sides: $8=6x + 8x+64$, which simplifies to $8 = 14x+64$.

Step5: Move constant to one side

Subtract 64 from both sides: $8-64=14x$, so $- 56=14x$.

Step6: Solve for x

Divide both sides by 14: $x=\frac{-56}{14}=-4$.

Answer:

$x = - 4$