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=−13 x equals negative 13 x=7 x equals 7 x=176 x equals Start Fraction 17 over 6 End Fraction x=−43
Answers
GPT-4o mini
In a rectangle, opposite sides are equal in length. Given that \( AO = 4x - 3 \) and \( BO = 5x - 10 \), we can set these two expressions equal to each other:
\[
4x - 3 = 5x - 10
\]
Now, let's solve for \( x \).
1. Rearranging the equation gives:
\[
4x - 5x = -10 + 3
\]
\[
-x = -7
\]
2. Multiplying both sides by -1:
\[
x = 7
\]
Thus, the value of \( x \) is \( 7 \).
The correct response is: \( x = 7 \).
\[
4x - 3 = 5x - 10
\]
Now, let's solve for \( x \).
1. Rearranging the equation gives:
\[
4x - 5x = -10 + 3
\]
\[
-x = -7
\]
2. Multiplying both sides by -1:
\[
x = 7
\]
Thus, the value of \( x \) is \( 7 \).
The correct response is: \( x = 7 \).