Question

7(x+4) = 5(x+2)
solving steps and properties used

Answer 1

To solve the equation \( 7(x + 4) = 5(x + 2) \), we will follow a series of steps using algebraic properties. Here are the steps along with the properties used:

1. **Distribute the terms**:
Use the distributive property \( a(b + c) = ab + ac \) to eliminate the parentheses on both sides.
\[
7(x + 4) = 7x + 28
\]
\[
5(x + 2) = 5x + 10
\]
After distribution, the equation becomes:
\[
7x + 28 = 5x + 10
\]

2. **Isolate the variable**:
To isolate \( x \), we want to get all the \( x \) terms on one side and the constant terms on the other. We can do this by subtracting \( 5x \) from both sides.
\[
7x + 28 - 5x = 5x + 10 - 5x
\]
This simplifies to:
\[
2x + 28 = 10
\]

3. **Subtract the constant term**:
Next, we will subtract \( 28 \) from both sides to isolate the term with \( x \).
\[
2x + 28 - 28 = 10 - 28
\]
This simplifies to:
\[
2x = -18
\]

4. **Solve for \( x \)**:
Finally, divide both sides by \( 2 \) to solve for \( x \):
\[
\frac{2x}{2} = \frac{-18}{2}
\]
This gives:
\[
x = -9
\]

So the solution to the equation is:
\[
\boxed{-9}
\]

### Summary of Properties Used:
- **Distributive Property**: To eliminate parentheses.
- **Addition and Subtraction Properties of Equality**: To move terms from one side of the equation to the other while keeping the equation balanced.
- **Division Property of Equality**: To isolate the variable and solve for \( x \).