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The problem involves a parallelogram ABCD where sides \(AB = 9x - 14\) inches and \(DC = 3x + 4\) inches. Since opposite sides of a parallelogram are equal, we know that:

\[
AB = DC
\]

This gives us the equation:

\[
9x - 14 = 3x + 4
\]

### Solving the equation:
1. Subtract \(3x\) from both sides:
   \[
   9x - 3x - 14 = 4
   \]
   \[
   6x - 14 = 4
   \]

2. Add 14 to both sides:
   \[
   6x = 18
   \]

3. Divide both sides by 6:
   \[
   x = 3
   \]

### Finding \(DC\):
Now, substitute \(x = 3\) into the expression for \(DC\):

\[
DC = 3x + 4 = 3(3) + 4 = 9 + 4 = 13 \text{ inches}
\]

Thus, \(DC = 13\) inches.

### Final Answer: \( \boxed{13} \text{ in.} \)

Would you like more details or have any other questions?

Here are 5 related questions to explore:
1. What properties of a parallelogram are used to solve problems like this?
2. How do you solve an equation involving variables on both sides?
3. How would you approach this problem if it involved a different quadrilateral?
4. How can you check the correctness of your solution in geometry?
5. What other geometric figures have congruent opposite sides?

**Tip:** Always verify that your final answer satisfies the conditions of the problem (like using properties of shapes).

In parallelogram ABCD, what is DC given that AB = 9x - 14 inches and DC = 3x + 4 inches?

Learn how to find the length of side DC in parallelogram ABCD, where AB = 9x - 14 inches and DC = 3x + 4 inches. This problem uses the property that opposite sides of a parallelogram are equal and covers algebraic manipulation for solving linear equations. Suitable for students in Grades 8-10.

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