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 a systematic plan. Here are the steps involved:

### Step 1: Simplify the Equation
The first step is to eliminate the negative sign in front of the parentheses. We can do this by multiplying both sides of the equation by -1:

\[
-34 = m + 3
\]

### Step 2: Isolate the Variable
Next, we want to isolate \( m \) on one side of the equation. To do this, we will subtract 3 from both sides:

\[
-34 - 3 = m
\]

### Step 3: Perform the Arithmetic
Now, we need to do the arithmetic on the left side of the equation:

\[
-34 - 3 = -37
\]

This gives us:

\[
m = -37
\]

### Step 4: Verify the Solution
Finally, it’s a good practice to check our solution by substituting \( m = -37 \) back into the original equation to ensure both sides are equal:

Substituting \( m = -37 \) into the original equation:

\[
34 = -((-37) + 3)
\]
This simplifies to:

\[
34 = -(-34)
\]
And further to:

\[
34 = 34
\]

### Conclusion
Since both sides of the original equation are equal when we substitute \( m = -37 \), we confirm that our solution is correct.

Thus, the solution to the equation \( 34 = -(m + 3) \) is:

\[
\boxed{-37}
\]