in parallelogram MNOP, the diagonals MO and NP intersect at point L. ML=x+7 and LO=2x-10. what is the value of x?

1 answer

In a parallelogram, the diagonals bisect each other. This means that segments ML and LO are equal in length.

Given:

  • \( ML = x + 7 \)
  • \( LO = 2x - 10 \)

Since ML = LO, we can set up the equation:

\[ x + 7 = 2x - 10 \]

To solve for \( x \), we will isolate \( x \) on one side. First, subtract \( x \) from both sides:

\[ 7 = x - 10 \]

Next, add 10 to both sides:

\[ 7 + 10 = x \] \[ x = 17 \]

Thus, the value of \( x \) is \( \boxed{17} \).