Solve for y: -12 = 3(y + 2) - 6y. Simplify your answer as much as possible.

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Understand the Problem

The question is asking us to solve the equation for y and simplify the answer as much as possible. We will approach this by isolating y on one side of the equation.

Answer

$$ y = 6 $$
Answer for screen readers

$$ y = 6 $$

Steps to Solve

  1. Distribute on the right side of the equation

First, we need to distribute $3$ across the expression $(y + 2)$.

$$ -12 = 3y + 6 - 6y $$

  1. Combine like terms

Next, combine the terms with $y$ on the right side. The equation now becomes:

$$ -12 = (3y - 6y) + 6 $$

This simplifies to:

$$ -12 = -3y + 6 $$

  1. Isolate the term with y

To isolate the term with $y$, subtract $6$ from both sides:

$$ -12 - 6 = -3y $$

This simplifies to:

$$ -18 = -3y $$

  1. Solve for y

Now, divide both sides by $-3$ to solve for $y$:

$$ y = \frac{-18}{-3} $$

This simplifies to:

$$ y = 6 $$

$$ y = 6 $$

More Information

The solution $y = 6$ means that when you substitute $6$ back into the original equation, both sides will be equal. This reinforces the validity of our solution.

Tips

  • Forgetting to distribute properly can lead to incorrect terms.
  • Not combining like terms accurately can result in errors in solving for $y$.
  • Miscalculating the signs when subtracting or dividing can lead to erroneous results.

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