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:
\[ \boxed{-37} \]
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