What is the solution to -(-5m + 11) = 3(m - 41)?
Understand the Problem
The question is asking for the solution to the equation involving the variable m, specifically to solve the equation -(-5m + 11) = 3(m - 41). This will involve distributing and simplifying the equation to isolate m.
Answer
$m = -56$
Answer for screen readers
The solution to the equation is $m = -56$.
Steps to Solve
- Distribute the negative sign on the left side
Start by distributing the negative sign across the expression:
$$ -(-5m + 11) = 5m - 11 $$
So, the equation becomes:
$$ 5m - 11 = 3(m - 41) $$
- Distribute the 3 on the right side
Distribute the 3 through the expression on the right side:
$$ 3(m - 41) = 3m - 123 $$
Now, we have:
$$ 5m - 11 = 3m - 123 $$
- Isolate the variable m
Subtract $3m$ from both sides to consolidate like terms:
$$ 5m - 3m - 11 = -123 $$
This simplifies to:
$$ 2m - 11 = -123 $$
Next, add 11 to both sides:
$$ 2m = -123 + 11 $$
Which simplifies to:
$$ 2m = -112 $$
- Solve for m
Divide both sides by 2 to find $m$:
$$ m = \frac{-112}{2} $$
Thus:
$$ m = -56 $$
The solution to the equation is $m = -56$.
More Information
This solution indicates that when you substitute $m = -56$ back into the original equation, both sides of the equation will be equal, confirming it as the correct solution.
Tips
- Forgetting to distribute the negative sign properly.
- Mixing up terms when combining like terms, which can lead to incorrect isolation of the variable.
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