Solve for w in the equation 37 = 5(w + 8) - 2w. Simplify your answer as much as possible.
Understand the Problem
The question is asking us to solve the equation 37 = 5(w + 8) - 2w for the variable w and simplify the answer as much as possible.
Answer
$w = -1$
Answer for screen readers
The solution for (w) is (w = -1).
Steps to Solve
- Distribute the 5
Start by distributing the 5 on the right side of the equation:
$$ 37 = 5(w + 8) - 2w $$
This gives us:
$$ 37 = 5w + 40 - 2w $$
- Combine like terms
Next, combine the (5w) and (-2w):
$$ 37 = (5w - 2w) + 40 $$
This simplifies to:
$$ 37 = 3w + 40 $$
- Isolate the variable w
Now, subtract 40 from both sides to isolate terms with (w):
$$ 37 - 40 = 3w $$
This results in:
$$ -3 = 3w $$
- Solve for w
Finally, divide both sides by 3 to solve for (w):
$$ w = \frac{-3}{3} $$
This simplifies to:
$$ w = -1 $$
The solution for (w) is (w = -1).
More Information
In this problem, we solved a linear equation involving distribution and combining like terms, which are fundamental skills in algebra. The final answer of (w = -1) indicates that if you plug this value back into the original equation, both sides will equal the same value.
Tips
- Neglecting to distribute: Sometimes students forget to distribute the term correctly, leading to incorrect simplifications.
- Miscombining terms: Confusing (5w) with (-2w) can also lead to mistakes; always treat signs carefully.
- Dividing incorrectly: Ensure that when you divide both sides by a number, the division is done on both sides of the equation.
