Solve for w in the equation 37 = 5(w + 8) - 2w. Simplify your answer as much as possible.

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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

  1. Distribute the 5

Start by distributing the 5 on the right side of the equation:

$$ 37 = 5(w + 8) - 2w $$

This gives us:

$$ 37 = 5w + 40 - 2w $$

  1. Combine like terms

Next, combine the (5w) and (-2w):

$$ 37 = (5w - 2w) + 40 $$

This simplifies to:

$$ 37 = 3w + 40 $$

  1. Isolate the variable w

Now, subtract 40 from both sides to isolate terms with (w):

$$ 37 - 40 = 3w $$

This results in:

$$ -3 = 3w $$

  1. 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.
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