Question
Find the value of x for which ABCD must be a parallelogram.
4x - 1
x + 26
9
8
35
5
Answers
GPT-4o
To determine the value of \( x \) for which \( ABCD \) is a parallelogram, we need to use the property that opposite sides of a parallelogram are equal in length.
Given:
- One pair of opposite sides is \( 4x - 1 \) and \( x + 26 \).
- We need to find when they are equal.
Set the expressions for the lengths of the opposite sides equal to each other:
\[ 4x - 1 = x + 26 \]
To solve for \( x \), first isolate \( x \) on one side of the equation:
1. Subtract \( x \) from both sides:
\[ 4x - x - 1 = x - x + 26 \]
\[ 3x - 1 = 26 \]
2. Add 1 to both sides:
\[ 3x - 1 + 1 = 26 + 1 \]
\[ 3x = 27 \]
3. Divide by 3:
\[ x = \frac{27}{3} \]
\[ x = 9 \]
So, the value of \( x \) for which \( ABCD \) must be a parallelogram is \( x = 9 \).
Given:
- One pair of opposite sides is \( 4x - 1 \) and \( x + 26 \).
- We need to find when they are equal.
Set the expressions for the lengths of the opposite sides equal to each other:
\[ 4x - 1 = x + 26 \]
To solve for \( x \), first isolate \( x \) on one side of the equation:
1. Subtract \( x \) from both sides:
\[ 4x - x - 1 = x - x + 26 \]
\[ 3x - 1 = 26 \]
2. Add 1 to both sides:
\[ 3x - 1 + 1 = 26 + 1 \]
\[ 3x = 27 \]
3. Divide by 3:
\[ x = \frac{27}{3} \]
\[ x = 9 \]
So, the value of \( x \) for which \( ABCD \) must be a parallelogram is \( x = 9 \).