Simplify the equation 4(y + 5) = -9y + 33 and solve for y.
Understand the Problem
The question is asking us to simplify the equation 4(y + 5) = -9y + 33 and solve for y. We will expand the left side, move terms involving y to one side, and constants to the other side to find the value of y.
Answer
$y = 1$
Answer for screen readers
The final answer is $y = 1$.
Steps to Solve
- Expand the left side of the equation
Distribute the 4 on the left side:
$$ 4(y + 5) = 4y + 20 $$
Now the equation looks like this:
$$ 4y + 20 = -9y + 33 $$
- Move terms involving y to one side
Add $9y$ to both sides to collect all $y$ terms on the left side:
$$ 4y + 9y + 20 = 33 $$
This simplifies to:
$$ 13y + 20 = 33 $$
- Move constants to the other side
Subtract 20 from both sides to isolate the term with $y$:
$$ 13y = 33 - 20 $$
This simplifies to:
$$ 13y = 13 $$
- Solve for y
Divide both sides by 13:
$$ y = \frac{13}{13} $$
This simplifies to:
$$ y = 1 $$
The final answer is $y = 1$.
More Information
This equation is a simple linear equation where the initial distribution and rearrangement are crucial steps. In solving linear equations, moving all variables to one side and constants to the other helps isolate the variable.
Tips
- Distributing Incorrectly: Make sure to correctly distribute when expanding terms.
- Combining Like Terms: Be careful when adding or subtracting the variables; errors here can lead to incorrect equations.
- Division by Zero: Always ensure that you are not inadvertently dividing by zero when simplifying.
