Question

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

Answer 1

To solve the equation \(8(2m + 3) = 120\) using inverse operations, let's break it down step by step.

1. **Distribute or simplify the equation.**
First, divide both sides of the equation by 8 to isolate the term with \(m\).

\[
2m + 3 = \frac{120}{8}
\]

Simplifying the right-hand side, we get:

\[
2m + 3 = 15
\]

2. **Subtract 3 from both sides.**
Next, we will subtract 3 from both sides to further isolate the term with \(m\).

\[
2m = 15 - 3
\]

Simplifying gives us:

\[
2m = 12
\]

3. **Divide by 2.**
Finally, divide both sides by 2 to solve for \(m\):

\[
m = \frac{12}{2}
\]

Simplifying this gives:

\[
m = 6
\]

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

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However, as I don't have the ability to utilize a sketch pad or create visual representations, I encourage you to sketch the work out as:
- Start with the original equation.
- Show each step with arrows indicating the operations performed, such as division and subtraction.
- Conclude with the final answer \(m = 6\).

If you have access to graphing tools or sketching software, you can illustrate the steps as outlined above to visualize the solution process!