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

Question

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:

\[ \boxed{-37} \]