Basic Math Examples

$2 t + \frac{4}{3} = \frac{11}{3} + \frac{19 t}{3}$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $\frac{19 t}{3}$ from both sides of the equation.

$2 t + \frac{4}{3} - \frac{19 t}{3} = \frac{11}{3}$

Step 1.2

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

$2 t \cdot \frac{3}{3} - \frac{19 t}{3} + \frac{4}{3} = \frac{11}{3}$

Step 1.3

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

$\frac{2 t \cdot 3}{3} - \frac{19 t}{3} + \frac{4}{3} = \frac{11}{3}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{2 t \cdot 3 - 19 t}{3} + \frac{4}{3} = \frac{11}{3}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{2 t \cdot 3 - 19 t + 4}{3} = \frac{11}{3}$

Step 1.6

Multiply $3$ by $2$ .

$\frac{6 t - 19 t + 4}{3} = \frac{11}{3}$

Step 1.7

Subtract $19 t$ from $6 t$ .

$\frac{- 13 t + 4}{3} = \frac{11}{3}$

Step 1.8

Factor $- 1$ out of $- 13 t$ .

$\frac{- (13 t) + 4}{3} = \frac{11}{3}$

Step 1.9

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{- (13 t) - 1 (- 4)}{3} = \frac{11}{3}$

Step 1.10

Factor $- 1$ out of $- (13 t) - 1 (- 4)$ .

$\frac{- (13 t - 4)}{3} = \frac{11}{3}$

Step 1.11

Rewrite $- (13 t - 4)$ as $- 1 (13 t - 4)$ .

$\frac{- 1 (13 t - 4)}{3} = \frac{11}{3}$

Step 1.12

Move the negative in front of the fraction.

$- \frac{13 t - 4}{3} = \frac{11}{3}$

Step 2

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

$- (13 t - 4) = 11$

Step 3

Simplify $- (13 t - 4)$ .

Tap for more steps...

Step 3.1

Apply the distributive property.

$- (13 t) - - 4 = 11$

Step 3.2

Multiply.

Tap for more steps...

Step 3.2.1

Multiply $13$ by $- 1$ .

$- 13 t - - 4 = 11$

Step 3.2.2

Multiply $- 1$ by $- 4$ .

$- 13 t + 4 = 11$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $4$ from both sides of the equation.

$- 13 t = 11 - 4$

Step 4.2

Subtract $4$ from $11$ .

$- 13 t = 7$

Step 5

Divide each term in $- 13 t = 7$ by $- 13$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $- 13 t = 7$ by $- 13$ .

$\frac{- 13 t}{- 13} = \frac{7}{- 13}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $- 13$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{- 13 t}{- 13} = \frac{7}{- 13}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t = \frac{7}{- 13}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Move the negative in front of the fraction.

$t = - \frac{7}{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{7}{13}$

Decimal Form:

$t = - 0.\overline{538461}$