Algebra Examples

$- \frac{3}{10} t = \frac{1}{2} (\frac{1}{5} t - 14) + \frac{1}{10} t$

Step 1

Since $t$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\frac{1}{2} \cdot (\frac{1}{5} t - 14) + \frac{1}{10} t = - \frac{3}{10} t$

Step 2

Simplify $\frac{1}{2} \cdot (\frac{1}{5} t - 14) + \frac{1}{10} t$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

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

$\frac{1}{2} \cdot (\frac{t}{5} - 14) + \frac{1}{10} t = - \frac{3}{10} t$

Step 2.1.2

Apply the distributive property.

$\frac{1}{2} \cdot \frac{t}{5} + \frac{1}{2} \cdot - 14 + \frac{1}{10} t = - \frac{3}{10} t$

Step 2.1.3

Multiply $\frac{1}{2} \cdot \frac{t}{5}$ .

Tap for more steps...

Step 2.1.3.1

Multiply $\frac{1}{2}$ by $\frac{t}{5}$ .

$\frac{t}{2 \cdot 5} + \frac{1}{2} \cdot - 14 + \frac{1}{10} t = - \frac{3}{10} t$

Step 2.1.3.2

Multiply $2$ by $5$ .

$\frac{t}{10} + \frac{1}{2} \cdot - 14 + \frac{1}{10} t = - \frac{3}{10} t$

Step 2.1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.4.1

Factor $2$ out of $- 14$ .

$\frac{t}{10} + \frac{1}{2} \cdot (2 (- 7)) + \frac{1}{10} t = - \frac{3}{10} t$

Step 2.1.4.2

Cancel the common factor.

$\frac{t}{10} + \frac{1}{2} \cdot (2 \cdot - 7) + \frac{1}{10} t = - \frac{3}{10} t$

Step 2.1.4.3

Rewrite the expression.

$\frac{t}{10} - 7 + \frac{1}{10} t = - \frac{3}{10} t$

Step 2.1.5

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

$\frac{t}{10} - 7 + \frac{t}{10} = - \frac{3}{10} t$

Step 2.2

Simplify terms.

Tap for more steps...

Step 2.2.1

Combine the numerators over the common denominator.

$- 7 + \frac{t + t}{10} = - \frac{3}{10} t$

Step 2.2.2

Add $t$ and $t$ .

$- 7 + \frac{2 t}{10} = - \frac{3}{10} t$

Step 2.2.3

Cancel the common factor of $2$ and $10$ .

Tap for more steps...

Step 2.2.3.1

Factor $2$ out of $2 t$ .

$- 7 + \frac{2 (t)}{10} = - \frac{3}{10} t$

Step 2.2.3.2

Cancel the common factors.

Tap for more steps...

Step 2.2.3.2.1

Factor $2$ out of $10$ .

$- 7 + \frac{2 t}{2 \cdot 5} = - \frac{3}{10} t$

Step 2.2.3.2.2

Cancel the common factor.

$- 7 + \frac{2 t}{2 \cdot 5} = - \frac{3}{10} t$

Step 2.2.3.2.3

Rewrite the expression.

$- 7 + \frac{t}{5} = - \frac{3}{10} t$

Step 3

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

Tap for more steps...

Step 3.1

Combine $t$ and $\frac{3}{10}$ .

$- 7 + \frac{t}{5} = - \frac{t \cdot 3}{10}$

Step 3.2

Move $3$ to the left of $t$ .

$- 7 + \frac{t}{5} = - \frac{3 t}{10}$

Step 4

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

Tap for more steps...

Step 4.1

Add $\frac{3 t}{10}$ to both sides of the equation.

$- 7 + \frac{t}{5} + \frac{3 t}{10} = 0$

Step 4.2

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

$- 7 + \frac{t}{5} \cdot \frac{2}{2} + \frac{3 t}{10} = 0$

Step 4.3

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

Tap for more steps...

Step 4.3.1

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

$- 7 + \frac{t \cdot 2}{5 \cdot 2} + \frac{3 t}{10} = 0$

Step 4.3.2

Multiply $5$ by $2$ .

$- 7 + \frac{t \cdot 2}{10} + \frac{3 t}{10} = 0$

Step 4.4

Combine the numerators over the common denominator.

$- 7 + \frac{t \cdot 2 + 3 t}{10} = 0$

Step 4.5

Add $t \cdot 2$ and $3 t$ .

Tap for more steps...

Step 4.5.1

Reorder $t$ and $2$ .

$- 7 + \frac{2 \cdot t + 3 t}{10} = 0$

Step 4.5.2

Add $2 \cdot t$ and $3 t$ .

$- 7 + \frac{5 \cdot t}{10} = 0$

Step 4.6

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

Tap for more steps...

Step 4.6.1

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

$- 7 + \frac{5 (t)}{10} = 0$

Step 4.6.2

Cancel the common factors.

Tap for more steps...

Step 4.6.2.1

Factor $5$ out of $10$ .

$- 7 + \frac{5 t}{5 \cdot 2} = 0$

Step 4.6.2.2

Cancel the common factor.

$- 7 + \frac{5 t}{5 \cdot 2} = 0$

Step 4.6.2.3

Rewrite the expression.

$- 7 + \frac{t}{2} = 0$

Step 5

Add $7$ to both sides of the equation.

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

Step 6

Multiply both sides of the equation by $2$ .

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

Step 7

Simplify both sides of the equation.

Tap for more steps...

Step 7.1

Simplify the left side.

Tap for more steps...

Step 7.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.1.1.1

Cancel the common factor.

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

Step 7.1.1.2

Rewrite the expression.

$t = 2 \cdot 7$

Step 7.2

Simplify the right side.

Tap for more steps...

Step 7.2.1

Multiply $2$ by $7$ .

$t = 14$