Question

4. Solve the equation justifying each step with the correct reasoning.

2(x+8)=2x+8
Step 1: Property to get simplified equation

Step 2: Property to get simplified equation

For this equation, there is/are

Answer 1

To solve the equation \( 2(x+8) = 2x + 8 \) and justify each step, we can follow these steps:

### Step 1: Distributive Property
Apply the distributive property to the left side of the equation.

\[
2(x+8) = 2 \cdot x + 2 \cdot 8
\]

This simplifies to:

\[
2x + 16 = 2x + 8
\]

### Step 2: Subtraction Property of Equality
Next, we can subtract \( 2x \) from both sides of the equation.

\[
2x + 16 - 2x = 2x + 8 - 2x
\]

This simplifies to:

\[
16 = 8
\]

### Reasoning
The first step uses the **Distributive Property** to expand \( 2(x+8) \). The second step uses the **Subtraction Property of Equality**, which states that if two quantities are equal, subtracting the same amount from both sides maintains equality.

### Conclusion
Now, we see that \( 16 = 8 \) is a false statement. This indicates that there are no values of \( x \) that will satisfy the original equation.

Thus, for this equation, there **is no solution**.