Solve for y: (3y-6)/9 = (4-2y)/-3
Understand the Problem
The question requires us to solve an algebraic equation for the variable 'y'. We need to isolate 'y' by performing algebraic operations on both sides of the equation, such as cross-multiplication and simplification.
Answer
$y = 2$
Answer for screen readers
$y=2$
Steps to Solve
- Cross-multiply to eliminate fractions
To get rid of the fractions, we'll cross-multiply. This means multiplying the numerator of the left side by the denominator of the right side, and vice versa.
$$ (3y - 6) \cdot (-3) = (4 - 2y) \cdot 9 $$
- Expand both sides of the equation
Now, we distribute the constants on both sides of the equation.
$$ -9y + 18 = 36 - 18y $$
- Isolate the 'y' terms
We want to get all the 'y' terms on one side of the equation. Let's add $18y$ to both sides.
$$ -9y + 18 + 18y = 36 - 18y + 18y $$
This simplifies to:
$$ 9y + 18 = 36 $$
- Isolate the constant terms
Now, we want to get all the constant terms on the other side of the equation. Subtract 18 from both sides.
$$ 9y + 18 - 18 = 36 - 18 $$
This simplifies to:
$$ 9y = 18 $$
- Solve for 'y'
Finally, we divide both sides by 9 to solve for 'y'.
$$ \frac{9y}{9} = \frac{18}{9} $$
Therefore,
$$ y = 2 $$
$y=2$
More Information
The solution to the equation $\frac{3y-6}{9}=\frac{4-2y}{-3}$ is $y=2$.
Tips
A common mistake is to incorrectly distribute the constants during the expansion of the equation. For example, forgetting to distribute the negative sign when multiplying $(3y - 6) \cdot (-3)$.
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