Algebra Examples

$\frac{2}{5} f + 2 = - \frac{1}{2} (8 + \frac{12}{5} f) - 6$

Step 1

Combine $\frac{2}{5}$ and $f$ .

$\frac{2 f}{5} + 2 = - \frac{1}{2} \cdot (8 + \frac{12}{5} f) - 6$

Step 2

Simplify $- \frac{1}{2} \cdot (8 + \frac{12}{5} f) - 6$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Combine $\frac{12}{5}$ and $f$ .

$\frac{2 f}{5} + 2 = - \frac{1}{2} \cdot (8 + \frac{12 f}{5}) - 6$

Step 2.1.2

Apply the distributive property.

$\frac{2 f}{5} + 2 = - \frac{1}{2} \cdot 8 - \frac{1}{2} \cdot \frac{12 f}{5} - 6$

Step 2.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{2 f}{5} + 2 = \frac{- 1}{2} \cdot 8 - \frac{1}{2} \cdot \frac{12 f}{5} - 6$

Step 2.1.3.2

Factor $2$ out of $8$ .

$\frac{2 f}{5} + 2 = \frac{- 1}{2} \cdot (2 (4)) - \frac{1}{2} \cdot \frac{12 f}{5} - 6$

Step 2.1.3.3

Cancel the common factor.

$\frac{2 f}{5} + 2 = \frac{- 1}{2} \cdot (2 \cdot 4) - \frac{1}{2} \cdot \frac{12 f}{5} - 6$

Step 2.1.3.4

Rewrite the expression.

$\frac{2 f}{5} + 2 = - 1 \cdot 4 - \frac{1}{2} \cdot \frac{12 f}{5} - 6$

Step 2.1.4

Multiply $- 1$ by $4$ .

$\frac{2 f}{5} + 2 = - 4 - \frac{1}{2} \cdot \frac{12 f}{5} - 6$

Step 2.1.5

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.5.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{2 f}{5} + 2 = - 4 + \frac{- 1}{2} \cdot \frac{12 f}{5} - 6$

Step 2.1.5.2

Factor $2$ out of $12 f$ .

$\frac{2 f}{5} + 2 = - 4 + \frac{- 1}{2} \cdot \frac{2 (6 f)}{5} - 6$

Step 2.1.5.3

Cancel the common factor.

$\frac{2 f}{5} + 2 = - 4 + \frac{- 1}{2} \cdot \frac{2 (6 f)}{5} - 6$

Step 2.1.5.4

Rewrite the expression.

$\frac{2 f}{5} + 2 = - 4 - 1 \frac{6 f}{5} - 6$

Step 2.1.6

Rewrite $- 1 \frac{6 f}{5}$ as $- \frac{6 f}{5}$ .

$\frac{2 f}{5} + 2 = - 4 - \frac{6 f}{5} - 6$

Step 2.2

Subtract $6$ from $- 4$ .

$\frac{2 f}{5} + 2 = - \frac{6 f}{5} - 10$

Step 3

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

Tap for more steps...

Step 3.1

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

$\frac{2 f}{5} + 2 + \frac{6 f}{5} = - 10$

Step 3.2

Combine the numerators over the common denominator.

$2 + \frac{2 f + 6 f}{5} = - 10$

Step 3.3

Add $2 f$ and $6 f$ .

$2 + \frac{8 f}{5} = - 10$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $2$ from both sides of the equation.

$\frac{8 f}{5} = - 10 - 2$

Step 4.2

Subtract $2$ from $- 10$ .

$\frac{8 f}{5} = - 12$

Step 5

Multiply both sides of the equation by $\frac{5}{8}$ .

$\frac{5}{8} \cdot \frac{8 f}{5} = \frac{5}{8} \cdot - 12$

Step 6

Simplify both sides of the equation.

Tap for more steps...

Step 6.1

Simplify the left side.

Tap for more steps...

Step 6.1.1

Simplify $\frac{5}{8} \cdot \frac{8 f}{5}$ .

Tap for more steps...

Step 6.1.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 6.1.1.1.1

Cancel the common factor.

$\frac{5}{8} \cdot \frac{8 f}{5} = \frac{5}{8} \cdot - 12$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{8} (8 f) = \frac{5}{8} \cdot - 12$

Step 6.1.1.2

Cancel the common factor of $8$ .

Tap for more steps...

Step 6.1.1.2.1

Factor $8$ out of $8 f$ .

$\frac{1}{8} (8 (f)) = \frac{5}{8} \cdot - 12$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{8} (8 f) = \frac{5}{8} \cdot - 12$

Step 6.1.1.2.3

Rewrite the expression.

$f = \frac{5}{8} \cdot - 12$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Simplify $\frac{5}{8} \cdot - 12$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 6.2.1.1.1

Factor $4$ out of $8$ .

$f = \frac{5}{4 (2)} \cdot - 12$

Step 6.2.1.1.2

Factor $4$ out of $- 12$ .

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

Step 6.2.1.1.3

Cancel the common factor.

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

Step 6.2.1.1.4

Rewrite the expression.

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

Step 6.2.1.2

Combine $\frac{5}{2}$ and $- 3$ .

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

Step 6.2.1.3

Simplify the expression.

Tap for more steps...

Step 6.2.1.3.1

Multiply $5$ by $- 3$ .

$f = \frac{- 15}{2}$

Step 6.2.1.3.2

Move the negative in front of the fraction.

$f = - \frac{15}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$f = - \frac{15}{2}$

Decimal Form:

$f = - 7.5$

Mixed Number Form:

$f = - 7 \frac{1}{2}$