Question

Generate a plan and describe the steps needed to solve the equation.

34 = –(m + 3)

Answer 1

To solve the equation \( 34 = -(m + 3) \), we can follow these steps:

### Step 1: Distribute the Negative Sign
The first step is to rewrite the equation by distributing the negative sign on the right-hand side.

\[
34 = -1 \cdot (m + 3)
\]

This gives us:

\[
34 = -m - 3
\]

### Step 2: Isolate the Variable Term
Next, we want to get all the terms involving \( m \) on one side and the constant terms on the other side. We can do this by adding 3 to both sides of the equation.

\[
34 + 3 = -m
\]

So, we have:

\[
37 = -m
\]

### Step 3: Solve for \( m \)
To solve for \( m \), we can multiply both sides of the equation by -1 to isolate \( m \).

\[
m = -37
\]

### Step 4: Verify the Solution
Finally, we can check our work by substituting \( m = -37 \) back into the original equation to ensure both sides are equal.

Starting with the original equation:

\[
34 = -(m + 3)
\]

Substituting \( m = -37 \):

\[
34 = -((-37) + 3)
\]
\[
34 = -(-34)
\]
\[
34 = 34
\]

Since both sides are equal, the solution is verified.

### Summary of Steps
1. Distribute the negative sign: \( 34 = -m - 3 \).
2. Isolate the variable: \( 37 = -m \).
3. Solve for \( m \): \( m = -37 \).
4. Verify the solution by substituting \( m \) back into the original equation.

The final solution is:

\[
\boxed{-37}
\]