Thank you for providing the answer choices. Let's solve the problem again with these options in mind.

**Question Summary:**  
The perimeter of the triangle is \(x\) units. The side lengths of the triangle are \(x-7\), \(x-6\), and \(x-5\). We need to find the value of \(x\).

### Step-by-Step Solution

1. **Perimeter Calculation:**  
   The perimeter of the triangle is given by the sum of its side lengths:
   \[
   \text{Perimeter} = (x - 7) + (x - 6) + (x - 5)
   \]

2. **Simplify the Expression:**  
   Combine like terms:
   \[
   \text{Perimeter} = x - 7 + x - 6 + x - 5 = 3x - 18
   \]

3. **Set Up the Equation:**  
   Since the perimeter is given as \(x\) units, we set up the equation:
   \[
   3x - 18 = x
   \]

4. **Solve for \(x\):**  
   Rearrange the equation:
   \[
   3x - x = 18
   \]
   \[
   2x = 18
   \]
   \[
   x = 9
   \]

It appears there might have been a slight misunderstanding in the answer choices provided earlier. Given the correct calculation, \(x = 9\). However, if the provided answer choices are **10, -10, 12, 15**, let's check which is correct:

**Re-evaluating Based on Choices:**

For \(x = 10\):
\[
\text{Perimeter} = 10 - 7 + 10 - 6 + 10 - 5 = 3 + 4 + 5 = 12
\]

For \(x = -10\):
\[
\text{Perimeter} = (-10) - 7 + (-10) - 6 + (-10) - 5 = -17 - 16 - 15 = -48 \, (\text{not a valid triangle})
\]

For \(x = 12\):
\[
\text{Perimeter} = 12 - 7 + 12 - 6 + 12 - 5 = 5 + 6 + 7 = 18 \, (\text{but perimeter is } x)
\]

For \(x = 15\):
\[
\text{Perimeter} = 15 - 7 + 15 - 6 + 15 - 5 = 8 + 9 + 10 = 27 \, (\text{but perimeter is } x)
\]

**Conclusion:**  
Based on our initial calculation, \(x = 9\) is correct. However, among the answer choices **10, -10, 12, 15**, only **\(x = 10\)** when plugged in gives a perimeter of 12, but this doesn't match the condition that the perimeter should be \(x\). Thus, based on the logical deduction here, the problem might need a correction for \(x = 9\).

Would you like more details or have any questions?

### Related Questions:

1. How can you determine if a set of numbers forms a valid triangle?
2. What is the formula for calculating the perimeter of different shapes?
3. How do we solve word problems involving algebraic expressions?
4. Why is it important to check all given answer choices?
5. How do different shapes' formulas for perimeter relate to one another?

**Tip:** Always double-check the problem statement and calculations to ensure all conditions are met before selecting an answer.

Learn how to calculate the perimeter of a triangle with sides given by expressions involving x. Solve the equation to find the value of x using step-by-step explanations and examples. Suitable for students in Grades 7-9.

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