Question
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?
Answers
GPT-4o mini
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 \( \boxed{17} \).
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 \( \boxed{17} \).