Question

given rectangle lmno below, lp = 44. if op = -2x + 2, solve for x.

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal and bisect each other. So $OP = \frac{1}{2}OL$ and $LP=\frac{1}{2}OL$, then $OP = LP/2$.

Step2: Set up the equation

Since $LP = 44$ and $OP=-2x + 2$, we have $-2x+2=\frac{44}{2}$.

Step3: Simplify the right - hand side

$\frac{44}{2}=22$, so the equation becomes $-2x + 2=22$.

Step4: Solve for x

Subtract 2 from both sides: $-2x=22 - 2$, so $-2x=20$. Then divide both sides by - 2: $x=\frac{20}{-2}=-10$.

Answer:

$x=-10$