Question
10 Numeric 1 point In parallelogram MATH, MH \( =3 x-7 \), and \( A T=2 x+1 \). Find the value(s) of \( x \). DRAW A PICTURE AND LABEL IT. SHOW WORK TO JUSTIFY YOUR ANSWER! Type your answer...
Ask by Conner Nguyen. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 8 \).
Solution
1. In parallelogram MATH, opposite sides are equal. Since side \( MH \) is opposite side \( AT \), we have:
\[
3x - 7 = 2x + 1
\]
2. Subtract \( 2x \) from both sides:
\[
x - 7 = 1
\]
3. Add 7 to both sides:
\[
x = 8
\]
4. Therefore, the value of \( x \) is \( 8 \).
5. Diagram of Parallelogram MATH:
\[
\begin{array}{ccc}
& A \quad \quad \quad \quad T \\
& \quad \quad \quad \quad \quad \quad \quad \\
M \quad \quad \quad \quad \quad \quad H \\
\end{array}
\]
- Label side \( AT \) (top side) with \( 2x+1 \).
- Label side \( MH \) (diagonally opposite to \( AT \)) with \( 3x-7 \).
(The diagram represents the parallelogram with vertices \( M \), \( A \), \( T \), and \( H \); note that the positions imply that opposite sides \( MH \) and \( AT \) are equal.)
Thus, \( x = 8 \) is the solution.
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Simplify this solution The Deep Dive
First additional information: In any parallelogram, opposite sides are equal in length. This means that for parallelogram MATH, we can set the lengths of MH and AT equal to each other. So, we can write the equation \(3x - 7 = 2x + 1\). Solving for \(x\) gives us the steps to isolate \(x\) and determine its value. Second additional information: Always remember to check your solution! After solving the equation, substitute \(x\) back into the expressions for MH and AT to verify that both lengths are indeed equal. This will help you avoid common mistakes and ensure your work is accurate. Enjoy drawing the parallelogram, labeling the sides, and making it visually clear!
