Solve for y: -12 = 3(y + 2) - 6y. Simplify your answer as much as possible.
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
- Distribute on the right side of the equation
First, we need to distribute $3$ across the expression $(y + 2)$.
$$ -12 = 3y + 6 - 6y $$
- Combine like terms
Next, combine the terms with $y$ on the right side. The equation now becomes:
$$ -12 = (3y - 6y) + 6 $$
This simplifies to:
$$ -12 = -3y + 6 $$
- Isolate the term with y
To isolate the term with $y$, subtract $6$ from both sides:
$$ -12 - 6 = -3y $$
This simplifies to:
$$ -18 = -3y $$
- 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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