Solve for t 2/3t-1/5t=2

$\frac{2}{3} t - \frac{1}{5} t = 2$

Simplify $\frac{2}{3} t - \frac{1}{5} t$ .

Simplify each term.

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

$\frac{2 t}{3} - \frac{1}{5} t = 2$

Combine $t$ and $\frac{1}{5}$ .

$\frac{2 t}{3} - \frac{t}{5} = 2$

To write $\frac{2 t}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 t}{3} \cdot \frac{5}{5} - \frac{t}{5} = 2$

To write $- \frac{t}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 t}{3} \cdot \frac{5}{5} - \frac{t}{5} \cdot \frac{3}{3} = 2$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 t}{3}$ by $\frac{5}{5}$ .

$\frac{2 t \cdot 5}{3 \cdot 5} - \frac{t}{5} \cdot \frac{3}{3} = 2$

Multiply $3$ by $5$ .

$\frac{2 t \cdot 5}{15} - \frac{t}{5} \cdot \frac{3}{3} = 2$

Multiply $\frac{t}{5}$ by $\frac{3}{3}$ .

$\frac{2 t \cdot 5}{15} - \frac{t \cdot 3}{5 \cdot 3} = 2$

Multiply $5$ by $3$ .

$\frac{2 t \cdot 5}{15} - \frac{t \cdot 3}{15} = 2$

Combine the numerators over the common denominator.

$\frac{2 t \cdot 5 - t \cdot 3}{15} = 2$

Simplify the numerator.

Factor $t$ out of $2 t \cdot 5 - t \cdot 3$ .

Factor $t$ out of $2 t \cdot 5$ .

$\frac{t (2 \cdot 5) - t \cdot 3}{15} = 2$

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

$\frac{t (2 \cdot 5) + t (- 1 \cdot 3)}{15} = 2$

Factor $t$ out of $t (2 \cdot 5) + t (- 1 \cdot 3)$ .

$\frac{t (2 \cdot 5 - 1 \cdot 3)}{15} = 2$

Multiply $2$ by $5$ .

$\frac{t (10 - 1 \cdot 3)}{15} = 2$

Multiply $- 1$ by $3$ .

$\frac{t (10 - 3)}{15} = 2$

Subtract $3$ from $10$ .

$\frac{t \cdot 7}{15} = 2$

Move $7$ to the left of $t$ .

$\frac{7 t}{15} = 2$

Multiply both sides of the equation by $\frac{15}{7}$ .

$\frac{15}{7} \cdot \frac{7 t}{15} = \frac{15}{7} \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{15}{7} \cdot \frac{7 t}{15}$ .

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15}{7} \cdot \frac{7 t}{15} = \frac{15}{7} \cdot 2$

Rewrite the expression.

$\frac{1}{7} (7 t) = \frac{15}{7} \cdot 2$

Cancel the common factor of $7$ .

Factor $7$ out of $7 t$ .

$\frac{1}{7} (7 (t)) = \frac{15}{7} \cdot 2$

Cancel the common factor.

$\frac{1}{7} (7 t) = \frac{15}{7} \cdot 2$

Rewrite the expression.

$t = \frac{15}{7} \cdot 2$

Simplify the right side.

Multiply $\frac{15}{7} \cdot 2$ .

Combine $\frac{15}{7}$ and $2$ .

$t = \frac{15 \cdot 2}{7}$

Multiply $15$ by $2$ .

$t = \frac{30}{7}$

The result can be shown in multiple forms.

Exact Form:

$t = \frac{30}{7}$

Decimal Form:

$t = 4.\overline{285714}$

Mixed Number Form:

$t = 4 \frac{2}{7}$

Solve for t 2/3t-1/5t=2

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