Solve the Inequality for f 8-4/5f>-14-2f

$8 - \frac{4}{5} f > - 14 - 2 f$

Step 1

Simplify each term.

Combine $f$ and $\frac{4}{5}$ .

$8 - \frac{f \cdot 4}{5} > - 14 - 2 f$

Move $4$ to the left of $f$ .

$8 - \frac{4 f}{5} > - 14 - 2 f$

Step 2

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

Add $2 f$ to both sides of the inequality.

$8 - \frac{4 f}{5} + 2 f > - 14$

To write $2 f$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$8 - \frac{4 f}{5} + 2 f \cdot \frac{5}{5} > - 14$

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

$8 - \frac{4 f}{5} + \frac{2 f \cdot 5}{5} > - 14$

Combine the numerators over the common denominator.

$8 + \frac{- 4 f + 2 f \cdot 5}{5} > - 14$

Simplify the numerator.

Factor $2 f$ out of $- 4 f + 2 f \cdot 5$ .

Factor $2 f$ out of $- 4 f$ .

$8 + \frac{2 f (- 2) + 2 f \cdot 5}{5} > - 14$

Factor $2 f$ out of $2 f \cdot 5$ .

$8 + \frac{2 f (- 2) + 2 f (5)}{5} > - 14$

Factor $2 f$ out of $2 f (- 2) + 2 f (5)$ .

$8 + \frac{2 f (- 2 + 5)}{5} > - 14$

Add $- 2$ and $5$ .

$8 + \frac{2 f \cdot 3}{5} > - 14$

Multiply $3$ by $2$ .

$8 + \frac{6 f}{5} > - 14$

Step 3

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

Subtract $8$ from both sides of the inequality.

$\frac{6 f}{5} > - 14 - 8$

Subtract $8$ from $- 14$ .

$\frac{6 f}{5} > - 22$

Step 4

Multiply both sides by $5$ .

$\frac{6 f}{5} \cdot 5 > - 22 \cdot 5$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{6 f}{5} \cdot 5 > - 22 \cdot 5$

Rewrite the expression.

$6 f > - 22 \cdot 5$

Simplify the right side.

Multiply $- 22$ by $5$ .

$6 f > - 110$

Step 6

Divide each term in $6 f > - 110$ by $6$ and simplify.

Divide each term in $6 f > - 110$ by $6$ .

$\frac{6 f}{6} > \frac{- 110}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 f}{6} > \frac{- 110}{6}$

Divide $f$ by $1$ .

$f > \frac{- 110}{6}$

Simplify the right side.

Cancel the common factor of $- 110$ and $6$ .

Factor $2$ out of $- 110$ .

$f > \frac{2 (- 55)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$f > \frac{2 \cdot - 55}{2 \cdot 3}$

Cancel the common factor.

$f > \frac{2 \cdot - 55}{2 \cdot 3}$

Rewrite the expression.

$f > \frac{- 55}{3}$

Move the negative in front of the fraction.

$f > - \frac{55}{3}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$f > - \frac{55}{3}$

Interval Notation:

$(- \frac{55}{3}, \infty)$

Solve the Inequality for f 8-4/5f>-14-2f

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