Precalculus Examples

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

Step 1

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

Tap for more steps...

Step 1.1

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

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

Step 1.2

Simplify terms.

Tap for more steps...

Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.3

Simplify the numerator.

Tap for more steps...

Step 1.3.1

Multiply $3$ by $3$ .

$\frac{9 t - 2 (t - 1)}{3} = 4$

Step 1.3.2

Apply the distributive property.

$\frac{9 t - 2 t - 2 \cdot - 1}{3} = 4$

Step 1.3.3

Multiply $- 2$ by $- 1$ .

$\frac{9 t - 2 t + 2}{3} = 4$

Step 1.3.4

Subtract $2 t$ from $9 t$ .

$\frac{7 t + 2}{3} = 4$

Step 2

Multiply both sides by $3$ .

$\frac{7 t + 2}{3} \cdot 3 = 4 \cdot 3$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

$\frac{7 t + 2}{3} \cdot 3 = 4 \cdot 3$

Step 3.1.1.2

Rewrite the expression.

$7 t + 2 = 4 \cdot 3$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $4$ by $3$ .

$7 t + 2 = 12$

Step 4

Solve for $t$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Subtract $2$ from both sides of the equation.

$7 t = 12 - 2$

Step 4.1.2

Subtract $2$ from $12$ .

$7 t = 10$

Step 4.2

Divide each term in $7 t = 10$ by $7$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $7 t = 10$ by $7$ .

$\frac{7 t}{7} = \frac{10}{7}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 t}{7} = \frac{10}{7}$

Step 4.2.2.1.2

Divide $t$ by $1$ .

$t = \frac{10}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{10}{7}$

Decimal Form:

$t = 1.\overline{428571}$

Mixed Number Form:

$t = 1 \frac{3}{7}$