Algebra Examples

$\frac{3}{4} t - \frac{5}{6} = \frac{2}{3} t$

Step 1

Combine $\frac{3}{4}$ and $t$ .

$\frac{3 t}{4} - \frac{5}{6} = \frac{2}{3} t$

Step 2

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

$\frac{3 t}{4} - \frac{5}{6} = \frac{2 t}{3}$

Step 3

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

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Step 3.1

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

$\frac{3 t}{4} - \frac{5}{6} - \frac{2 t}{3} = 0$

Step 3.2

To write $\frac{3 t}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 t}{4} \cdot \frac{3}{3} - \frac{2 t}{3} - \frac{5}{6} = 0$

Step 3.3

To write $- \frac{2 t}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 t}{4} \cdot \frac{3}{3} - \frac{2 t}{3} \cdot \frac{4}{4} - \frac{5}{6} = 0$

Step 3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{3 t}{4}$ by $\frac{3}{3}$ .

$\frac{3 t \cdot 3}{4 \cdot 3} - \frac{2 t}{3} \cdot \frac{4}{4} - \frac{5}{6} = 0$

Step 3.4.2

Multiply $4$ by $3$ .

$\frac{3 t \cdot 3}{12} - \frac{2 t}{3} \cdot \frac{4}{4} - \frac{5}{6} = 0$

Step 3.4.3

Multiply $\frac{2 t}{3}$ by $\frac{4}{4}$ .

$\frac{3 t \cdot 3}{12} - \frac{2 t \cdot 4}{3 \cdot 4} - \frac{5}{6} = 0$

Step 3.4.4

Multiply $3$ by $4$ .

$\frac{3 t \cdot 3}{12} - \frac{2 t \cdot 4}{12} - \frac{5}{6} = 0$

Step 3.5

Combine the numerators over the common denominator.

$\frac{3 t \cdot 3 - 2 t \cdot 4}{12} - \frac{5}{6} = 0$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor $t$ out of $3 t \cdot 3 - 2 t \cdot 4$ .

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Step 3.6.1.1.1

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

$\frac{t (3 \cdot 3) - 2 t \cdot 4}{12} - \frac{5}{6} = 0$

Step 3.6.1.1.2

Factor $t$ out of $- 2 t \cdot 4$ .

$\frac{t (3 \cdot 3) + t (- 2 \cdot 4)}{12} - \frac{5}{6} = 0$

Step 3.6.1.1.3

Factor $t$ out of $t (3 \cdot 3) + t (- 2 \cdot 4)$ .

$\frac{t (3 \cdot 3 - 2 \cdot 4)}{12} - \frac{5}{6} = 0$

Step 3.6.1.2

Multiply $3$ by $3$ .

$\frac{t (9 - 2 \cdot 4)}{12} - \frac{5}{6} = 0$

Step 3.6.1.3

Multiply $- 2$ by $4$ .

$\frac{t (9 - 8)}{12} - \frac{5}{6} = 0$

Step 3.6.1.4

Subtract $8$ from $9$ .

$\frac{t \cdot 1}{12} - \frac{5}{6} = 0$

Step 3.6.2

Multiply $t$ by $1$ .

$\frac{t}{12} - \frac{5}{6} = 0$

Step 4

Add $\frac{5}{6}$ to both sides of the equation.

$\frac{t}{12} = \frac{5}{6}$

Step 5

Multiply both sides of the equation by $12$ .

$12 \frac{t}{12} = 12 (\frac{5}{6})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $12$ .

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Step 6.1.1.1

Cancel the common factor.

$12 \frac{t}{12} = 12 (\frac{5}{6})$

Step 6.1.1.2

Rewrite the expression.

$t = 12 (\frac{5}{6})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $12 (\frac{5}{6})$ .

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Step 6.2.1.1

Cancel the common factor of $6$ .

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Step 6.2.1.1.1

Factor $6$ out of $12$ .

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

Step 6.2.1.1.2

Cancel the common factor.

$t = 6 \cdot 2 \frac{5}{6}$

Step 6.2.1.1.3

Rewrite the expression.

$t = 2 \cdot 5$

Step 6.2.1.2

Multiply $2$ by $5$ .

$t = 10$