Parallelogram X Value 7Dcc01

1. **State the problem:** We are given a parallelogram $TUVW$ with diagonals intersecting at point $S$. The segments $ST$ and $SV$ are parts of the diagonals. 2. **Important property:** In a parallelogram, the diagonals bisect each other. This means that $S$ is the midpoint of both diagonals, so $ST = SV$. 3. **Set up the equation:** Since $ST = SV$, we have: $$2x + 31 = 7x + 26$$ 4. **Solve for $x$:** Subtract $2x$ from both sides: $$\cancel{2x} + 31 = 7x - \cancel{2x} + 26 \implies 31 = 5x + 26$$ Subtract $26$ from both sides: $$31 - 26 = 5x + \cancel{26} - \cancel{26} \implies 5 = 5x$$ Divide both sides by $5$: $$\frac{5}{\cancel{5}} = \frac{5x}{\cancel{5}} \implies 1 = x$$ 5. **Final answer:** $$\boxed{1}$$ Thus, the value of $x$ is $1$.