Solve for t 3/5t-1/10t=t-5/2

$\frac{3}{5} t - \frac{1}{10} t = t - \frac{5}{2}$

Step 1

Simplify $\frac{3}{5} t - \frac{1}{10} t$ .

Simplify each term.

Combine $\frac{3}{5}$ and $t$ .

$\frac{3 t}{5} - \frac{1}{10} t = t - \frac{5}{2}$

Combine $t$ and $\frac{1}{10}$ .

$\frac{3 t}{5} - \frac{t}{10} = t - \frac{5}{2}$

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

$\frac{3 t}{5} \cdot \frac{2}{2} - \frac{t}{10} = t - \frac{5}{2}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{3 t \cdot 2}{5 \cdot 2} - \frac{t}{10} = t - \frac{5}{2}$

Multiply $5$ by $2$ .

$\frac{3 t \cdot 2}{10} - \frac{t}{10} = t - \frac{5}{2}$

Combine the numerators over the common denominator.

$\frac{3 t \cdot 2 - t}{10} = t - \frac{5}{2}$

Simplify the numerator.

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

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

$\frac{t (3 \cdot 2) - t}{10} = t - \frac{5}{2}$

Factor $t$ out of $- t$ .

$\frac{t (3 \cdot 2) + t \cdot - 1}{10} = t - \frac{5}{2}$

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

$\frac{t (3 \cdot 2 - 1)}{10} = t - \frac{5}{2}$

Multiply $3$ by $2$ .

$\frac{t (6 - 1)}{10} = t - \frac{5}{2}$

Subtract $1$ from $6$ .

$\frac{t \cdot 5}{10} = t - \frac{5}{2}$

Cancel the common factor of $5$ and $10$ .

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

$\frac{5 \cdot t}{10} = t - \frac{5}{2}$

Cancel the common factors.

Factor $5$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

Subtract $t$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

Raise $t$ to the power of $1$ .

$\frac{t^{1} - t \cdot 2}{2} = - \frac{5}{2}$

Factor $t$ out of $t^{1}$ .

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

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

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

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

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

Multiply $- 1$ by $2$ .

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

Subtract $2$ from $1$ .

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

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

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

Move the negative in front of the fraction.

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

Step 3

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

$- t = - 5$

Step 4

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 3/5t-1/10t=t-5/2

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