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

Understand the Problem

The question is asking to solve the equation -12 = 3(y + 2) - 6y for the variable y and simplify the answer as much as possible.

Answer

The solution is $ y = 6 $.

Steps to Solve

Distribute the 3 First, distribute the 3 on the right side of the equation:

$$ -12 = 3(y + 2) - 6y $$

This expands to:

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

Combine like terms Next, combine the like terms on the right side:

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

This simplifies to:

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

Isolate the term with y Now, subtract 6 from both sides of the equation:

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

Which simplifies to:

$$ -3y = -18 $$

Solve for y Finally, divide both sides by -3:

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

This simplifies to:

$$ y = 6 $$

The solution for the equation is ( y = 6 ).

More Information

The value of ( y ) indicates that after substituting back into the original equation, both sides will equal, showing that the solution is correct. Solving linear equations is a fundamental concept in algebra, useful in various applications.

Tips

Misdistributing: Ensure you distribute correctly; missing a term can lead to errors.
Combining terms incorrectly: Always carefully combine like terms on each side.
Sign errors: Be cautious with positive and negative signs when isolating variables.

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