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Solve for $t$ . $\newline$ $3\left(\frac{1}{3}t + \frac{2}{3}\right) = 4t - 2$ $\newline$ $t =$ __

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Solve multi-step equations with fractional coefficients

Full solution

Q. Solve for

t

.

\newline

3\left(\frac{1}{3}t + \frac{2}{3}\right) = 4t - 2

\newline

t =

__

Distribute Values: Distribute $3$ to each term inside the parentheses. $\newline$ $3 \times (\frac{1}{3}t + \frac{2}{3}) = 3 \times \frac{1}{3}t + 3 \times \frac{2}{3}$ $\newline$ $= t + 2$
Set Up Equation: Set up the equation with the distributed values. $t + 2 = 4t - 2$
Isolate Variable: Isolate $t$ by subtracting $t$ from both sides. $\newline$ $t + 2 - t = 4t - t - 2$ $\newline$ $2 = 3t - 2$
Add to Isolate: Add $2$ to both sides to further isolate $3t$ . $\newline$ $2 + 2 = 3t - 2 + 2$ $\newline$ $4 = 3t$
Divide to Solve: Divide both sides by $3$ to solve for $t$ . $\newline$ $\frac{4}{3} = \frac{3t}{3}$ $\newline$ $t = \frac{4}{3}$

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