Question

Solve using inverse operations. Use the sketch pad to show your work:
8(2m+3)=120


MUST show your work.

Answer 1

To solve the equation \( 8(2m + 3) = 120 \) using inverse operations, follow these steps:

### Step 1: Distribute the 8
First, distribute the 8 to the terms inside the parentheses:

\[
8 \cdot 2m + 8 \cdot 3 = 120
\]

This simplifies to:

\[
16m + 24 = 120
\]

### Step 2: Subtract 24 from both sides
Next, we want to isolate the term with \( m \). To do this, subtract 24 from both sides of the equation:

\[
16m + 24 - 24 = 120 - 24
\]

This simplifies to:

\[
16m = 96
\]

### Step 3: Divide by 16
Now, divide both sides by 16 to solve for \( m \):

\[
\frac{16m}{16} = \frac{96}{16}
\]

This gives us:

\[
m = 6
\]

### Conclusion
The solution to the equation \( 8(2m + 3) = 120 \) is \( m = 6 \).

### Summary of Steps
1. Distribute: \( 8(2m + 3) \rightarrow 16m + 24 \)
2. Subtract: \( 16m + 24 - 24 \rightarrow 16m = 96 \)
3. Divide: \( \frac{16m}{16} \rightarrow m = 6 \)

If you were using a sketch pad, you could represent each step as a visual, showing both sides of the equation during each operation, clearly indicating the operations performed (distribution, subtraction, and division). If you have any further questions or need more detail, feel free to ask!