Question

Given that ABCD
is a rectangle with AO=4x−3
and BO=5x−10
, what is the value of x?

(1 point)
Responses

x=−43
x equals negative Start Fraction 4 over 3 End Fraction

x=7
x equals 7

x=−13
x equals negative 13

x=176

Answer 1

To solve for \( x \) in the rectangle \( ABCD \) where \( AO = 4x - 3 \) and \( BO = 5x - 10 \), we will first recognize that in a rectangle, opposite sides are equal. Therefore, we set \( AO \) equal to \( BO \):

\[
4x - 3 = 5x - 10
\]

Now, we will solve for \( x \).

1. Subtract \( 4x \) from both sides:

\[
-3 = x - 10
\]

2. Add \( 10 \) to both sides:

\[
7 = x
\]

Thus, \( x = 7 \).

The correct answer is:

\[
\text{x equals 7}
\]