Question

7(x+4) = 5(x+2)

give me 4 of the solving steps and 4 of the property used

Answer 1

Let's solve the equation \( 7(x+4) = 5(x+2) \) step by step and identify the properties used.

### Solving Steps:

1. **Distribute the Terms**:
\[
7(x+4) = 7x + 28 \quad \text{and} \quad 5(x+2) = 5x + 10
\]
So, the equation becomes:
\[
7x + 28 = 5x + 10
\]

2. **Isolate the Variable**:
Subtract \( 5x \) from both sides:
\[
7x - 5x + 28 = 10
\]
Simplifying this gives:
\[
2x + 28 = 10
\]

3. **Move the Constant**:
Subtract 28 from both sides:
\[
2x + 28 - 28 = 10 - 28
\]
This simplifies to:
\[
2x = -18
\]

4. **Solve for \( x \)**:
Divide both sides by 2:
\[
x = \frac{-18}{2} = -9
\]

### Properties Used:

1. **Distributive Property**:
Used to expand \( 7(x+4) \) and \( 5(x+2) \) to \( 7x + 28 \) and \( 5x + 10 \), respectively.

2. **Subtraction Property of Equality**:
Used when subtracting \( 5x \) from both sides and when subtracting 28 from both sides to maintain equality.

3. **Addition Property of Equality**:
(Not directly used in these steps, but often required when you would add a term to both sides to isolate a variable, as shown when moving constants.)

4. **Division Property of Equality**:
Used when dividing both sides by 2 to solve for \( x \).

Thus, by following these steps and applying these properties, we found that \( x = -9 \).