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Solve for $y$ . $\newline$ $-2 + y = 2(\frac{1}{3}y - 3)$ $\newline$ $y =$ __

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Solve multi-step equations with fractional coefficients

Full solution

Q. Solve for

y

.

\newline

-2 + y = 2(\frac{1}{3}y - 3)

\newline

y =

__

Distribute and Simplify: Distribute $2$ into the parentheses on the right side of the equation. $\newline$ $-2 + y = 2 \times \left(\frac{1}{3}y\right) - 2 \times 3$ $\newline$ $-2 + y = \frac{2}{3}y - 6$
Addition to Simplify: Add $2$ to both sides to simplify. $\newline$ $-2 + 2 + y = \frac{2}{3}y - 6 + 2$ $\newline$ $y = \frac{2}{3}y - 4$
Subtract to Isolate y: Subtract $\frac{2}{3}y$ from both sides to isolate $y$ . $\newline$ $y - \frac{2}{3}y = \frac{2}{3}y - \frac{2}{3}y - 4$ $\newline$ $\frac{1}{3}y = -4$
Multiply to Solve for y: Multiply both sides by $3$ to solve for $y$ . $3 \times \left(\frac{1}{3}y\right) = 3 \times -4$ $y = -12$

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