Algebra Examples

$\frac{2}{3} f - 3 = - 1 + \frac{4}{9} f + \frac{4}{9} f + 6$

Step 1

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

$- 1 + \frac{4}{9} f + \frac{4}{9} f + 6 = \frac{2}{3} f - 3$

Step 2

Simplify $- 1 + \frac{4}{9} f + \frac{4}{9} f + 6$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Combine $\frac{4}{9}$ and $f$ .

$- 1 + \frac{4 f}{9} + \frac{4}{9} f + 6 = \frac{2}{3} f - 3$

Step 2.1.2

Combine $\frac{4}{9}$ and $f$ .

$- 1 + \frac{4 f}{9} + \frac{4 f}{9} + 6 = \frac{2}{3} f - 3$

Step 2.2

Simplify terms.

Tap for more steps...

Step 2.2.1

Combine the numerators over the common denominator.

$- 1 + 6 + \frac{4 f + 4 f}{9} = \frac{2}{3} f - 3$

Step 2.2.2

Add $4 f$ and $4 f$ .

$- 1 + 6 + \frac{8 f}{9} = \frac{2}{3} f - 3$

Step 2.2.3

Add $- 1$ and $6$ .

$5 + \frac{8 f}{9} = \frac{2}{3} f - 3$

Step 3

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

$5 + \frac{8 f}{9} = \frac{2 f}{3} - 3$

Step 4

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

Tap for more steps...

Step 4.1

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

$5 + \frac{8 f}{9} - \frac{2 f}{3} = - 3$

Step 4.2

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

$5 + \frac{8 f}{9} - \frac{2 f}{3} \cdot \frac{3}{3} = - 3$

Step 4.3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.3.1

Multiply $\frac{2 f}{3}$ by $\frac{3}{3}$ .

$5 + \frac{8 f}{9} - \frac{2 f \cdot 3}{3 \cdot 3} = - 3$

Step 4.3.2

Multiply $3$ by $3$ .

$5 + \frac{8 f}{9} - \frac{2 f \cdot 3}{9} = - 3$

Step 4.4

Combine the numerators over the common denominator.

$5 + \frac{8 f - 2 f \cdot 3}{9} = - 3$

Step 4.5

Simplify the numerator.

Tap for more steps...

Step 4.5.1

Factor $2 f$ out of $8 f - 2 f \cdot 3$ .

Tap for more steps...

Step 4.5.1.1

Factor $2 f$ out of $8 f$ .

$5 + \frac{2 f (4) - 2 f \cdot 3}{9} = - 3$

Step 4.5.1.2

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

$5 + \frac{2 f (4) + 2 f (- 1 \cdot 3)}{9} = - 3$

Step 4.5.1.3

Factor $2 f$ out of $2 f (4) + 2 f (- 1 \cdot 3)$ .

$5 + \frac{2 f (4 - 1 \cdot 3)}{9} = - 3$

Step 4.5.2

Multiply $- 1$ by $3$ .

$5 + \frac{2 f (4 - 3)}{9} = - 3$

Step 4.5.3

Subtract $3$ from $4$ .

$5 + \frac{2 f \cdot 1}{9} = - 3$

Step 4.5.4

Multiply $2$ by $1$ .

$5 + \frac{2 f}{9} = - 3$

Step 5

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

Tap for more steps...

Step 5.1

Subtract $5$ from both sides of the equation.

$\frac{2 f}{9} = - 3 - 5$

Step 5.2

Subtract $5$ from $- 3$ .

$\frac{2 f}{9} = - 8$

Step 6

Multiply both sides of the equation by $\frac{9}{2}$ .

$\frac{9}{2} \cdot \frac{2 f}{9} = \frac{9}{2} \cdot - 8$

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

Simplify $\frac{9}{2} \cdot \frac{2 f}{9}$ .

Tap for more steps...

Step 7.1.1.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 7.1.1.1.1

Cancel the common factor.

$\frac{9}{2} \cdot \frac{2 f}{9} = \frac{9}{2} \cdot - 8$

Step 7.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 f) = \frac{9}{2} \cdot - 8$

Step 7.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.1.1.2.1

Factor $2$ out of $2 f$ .

$\frac{1}{2} (2 (f)) = \frac{9}{2} \cdot - 8$

Step 7.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 f) = \frac{9}{2} \cdot - 8$

Step 7.1.1.2.3

Rewrite the expression.

$f = \frac{9}{2} \cdot - 8$

Step 7.2

Simplify the right side.

Tap for more steps...

Step 7.2.1

Simplify $\frac{9}{2} \cdot - 8$ .

Tap for more steps...

Step 7.2.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.2.1.1.1

Factor $2$ out of $- 8$ .

$f = \frac{9}{2} \cdot (2 (- 4))$

Step 7.2.1.1.2

Cancel the common factor.

$f = \frac{9}{2} \cdot (2 \cdot - 4)$

Step 7.2.1.1.3

Rewrite the expression.

$f = 9 \cdot - 4$

Step 7.2.1.2

Multiply $9$ by $- 4$ .

$f = - 36$