Solve for t 1/2t-2/3=1/6+2/3t

$\frac{1}{2} t - \frac{2}{3} = \frac{1}{6} + \frac{2}{3} t$

Combine $\frac{1}{2}$ and $t$ .

$\frac{t}{2} - \frac{2}{3} = \frac{1}{6} + \frac{2}{3} t$

Combine $\frac{2}{3}$ and $t$ .

$\frac{t}{2} - \frac{2}{3} = \frac{1}{6} + \frac{2 t}{3}$

Move all terms containing $t$ to the left side of the equation.

Subtract $\frac{2 t}{3}$ from both sides of the equation.

$\frac{t}{2} - \frac{2}{3} - \frac{2 t}{3} = \frac{1}{6}$

To write $\frac{t}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{t}{2} \cdot \frac{3}{3} - \frac{2 t}{3} - \frac{2}{3} = \frac{1}{6}$

To write $- \frac{2 t}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{t}{2} \cdot \frac{3}{3} - \frac{2 t}{3} \cdot \frac{2}{2} - \frac{2}{3} = \frac{1}{6}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{t}{2}$ by $\frac{3}{3}$ .

$\frac{t \cdot 3}{2 \cdot 3} - \frac{2 t}{3} \cdot \frac{2}{2} - \frac{2}{3} = \frac{1}{6}$

Multiply $2$ by $3$ .

$\frac{t \cdot 3}{6} - \frac{2 t}{3} \cdot \frac{2}{2} - \frac{2}{3} = \frac{1}{6}$

Multiply $\frac{2 t}{3}$ by $\frac{2}{2}$ .

$\frac{t \cdot 3}{6} - \frac{2 t \cdot 2}{3 \cdot 2} - \frac{2}{3} = \frac{1}{6}$

Multiply $3$ by $2$ .

$\frac{t \cdot 3}{6} - \frac{2 t \cdot 2}{6} - \frac{2}{3} = \frac{1}{6}$

Combine the numerators over the common denominator.

$\frac{t \cdot 3 - 2 t \cdot 2}{6} - \frac{2}{3} = \frac{1}{6}$

Simplify each term.

Simplify the numerator.

Factor $t$ out of $t \cdot 3 - 2 t \cdot 2$ .

Factor $t$ out of $t \cdot 3$ .

$\frac{t (3) - 2 t \cdot 2}{6} - \frac{2}{3} = \frac{1}{6}$

Factor $t$ out of $- 2 t \cdot 2$ .

$\frac{t (3) + t (- 2 \cdot 2)}{6} - \frac{2}{3} = \frac{1}{6}$

Factor $t$ out of $t (3) + t (- 2 \cdot 2)$ .

$\frac{t (3 - 2 \cdot 2)}{6} - \frac{2}{3} = \frac{1}{6}$

Multiply $- 2$ by $2$ .

$\frac{t (3 - 4)}{6} - \frac{2}{3} = \frac{1}{6}$

Subtract $4$ from $3$ .

$\frac{t \cdot - 1}{6} - \frac{2}{3} = \frac{1}{6}$

Move $- 1$ to the left of $t$ .

$\frac{- 1 \cdot t}{6} - \frac{2}{3} = \frac{1}{6}$

Move the negative in front of the fraction.

$- \frac{t}{6} - \frac{2}{3} = \frac{1}{6}$

Move all terms not containing $t$ to the right side of the equation.

Add $\frac{2}{3}$ to both sides of the equation.

$- \frac{t}{6} = \frac{1}{6} + \frac{2}{3}$

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{t}{6} = \frac{1}{6} + \frac{2}{3} \cdot \frac{2}{2}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$- \frac{t}{6} = \frac{1}{6} + \frac{2 \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$- \frac{t}{6} = \frac{1}{6} + \frac{2 \cdot 2}{6}$

Combine the numerators over the common denominator.

$- \frac{t}{6} = \frac{1 + 2 \cdot 2}{6}$

Simplify the numerator.

Multiply $2$ by $2$ .

$- \frac{t}{6} = \frac{1 + 4}{6}$

Add $1$ and $4$ .

$- \frac{t}{6} = \frac{5}{6}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- t = 5$

Divide each term in $- t = 5$ by $- 1$ and simplify.

Divide each term in $- t = 5$ by $- 1$ .

$\frac{- t}{- 1} = \frac{5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{t}{1} = \frac{5}{- 1}$

Divide $t$ by $1$ .

$t = \frac{5}{- 1}$

Simplify the right side.

Divide $5$ by $- 1$ .

$t = - 5$

Solve for t 1/2t-2/3=1/6+2/3t

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