https://file.aiquickdraw.com/mathbot/file/172683933794796y7zujn.jpg

Let's go through each step of solving the equation:

### Equation:
\[
\frac{x - 7}{2} = -11
\]

#### Step-by-step reasoning:

1. **Step 1**:  
   The given equation is \(\frac{x - 7}{2} = -11\).  
   **Reason**: "Given equation"

2. **Step 2**:  
   The equation becomes:
   \[
   2 \cdot \frac{x - 7}{2} = -11 \cdot 2
   \]
   **Reason**: "Multiplication property of equality" (You multiply both sides by 2 to eliminate the fraction)

3. **Step 3**:  
   This simplifies to:
   \[
   x - 7 = -22
   \]
   **Reason**: "Simplification" (You simplified both sides)

4. **Step 4**:  
   Add 7 to both sides:
   \[
   x - 7 + 7 = -22 + 7
   \]
   **Reason**: "Addition property of equality" (You add 7 to both sides to isolate \(x\))

5. **Step 5**:  
   The result is:
   \[
   x = -15
   \]
   **Reason**: "Simplification" (You simplified both sides)

---

Would you like more details on any step? Here are five related questions for further practice:

1. How can you check if the solution \(x = -15\) is correct?
2. What would happen if you multiplied both sides by a negative number instead of 2?
3. What are the steps for solving similar equations with variables in the denominator?
4. How would the steps change if the equation was \(\frac{x + 7}{2} = -11\)?
5. What is the importance of the properties of equality in solving equations?

**Tip**: Always remember to check your final solution by substituting it back into the original equation!

The equation (x - 7) / 2 = -11 is solved in several steps. For each step, choose the reason that best justifies it.

Learn how to solve the linear equation (x - 7) / 2 = -11 using multiplication and addition properties of equality. This step-by-step guide simplifies the equation to find x = -15, suitable for students in Grades 7-8.

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