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I see you've uploaded an image containing a math problem with some missing steps. Let's work through it together, filling in the blanks.

The equation given is:

\[
4x + 12 = 7x - 24
\]

### Step-by-Step Solution:
1. **First**, apply the **distributive property** to remove the parentheses by multiplying \( x \) and \( 3 \) by 4. This step is already done, so we don't need to add it here. The equation becomes:
   \[
   4x + 12 = 7x - 24
   \]

2. **Next**, apply the **subtraction property of equality** to collect the variable terms on the right side. We subtract \( 4x \) from both sides of the equation:
   \[
   12 = 3x - 24
   \]

3. **Then**, apply the **addition property of equality** to isolate the variable term on the right side. We add 24 to both sides:
   \[
   36 = 3x
   \]

4. **Lastly**, apply the **division property of equality** to isolate the variable by dividing both sides by 3:
   \[
   x = 12
   \]

The blanks in the text can be filled as:
1. **distributive property**.
2. **subtraction property of equality**.
3. **addition property of equality**.
4. **division property of equality**.

Thus, the solution to the equation is \( x = 12 \).

---

Would you like more details on any of the steps or have any questions?

Here are 5 related questions for you:
1. What is the distributive property and when is it applied?
2. How do you decide which terms to move when solving an equation?
3. What other techniques can be used to isolate variables in different equations?
4. Can this method be used to solve systems of equations?
5. What is the purpose of applying properties like subtraction or addition to both sides?

**Tip**: Always perform the same operation on both sides of an equation to keep it balanced!

Learn how to solve the linear equation 4x + 12 = 7x - 24 step by step. This solution involves applying properties of equality, such as subtraction, addition, and division. Perfect for students in Grades 6-8.

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