Solve for f 8+10f>14-2f

$8 + 10 f > 14 - 2 f$

Step 1

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

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

$8 + 10 f + 2 f > 14$

Add $10 f$ and $2 f$ .

$8 + 12 f > 14$

Step 2

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

Subtract $8$ from both sides of the inequality.

$12 f > 14 - 8$

Subtract $8$ from $14$ .

$12 f > 6$

Step 3

Divide each term in $12 f > 6$ by $12$ and simplify.

Divide each term in $12 f > 6$ by $12$ .

$\frac{12 f}{12} > \frac{6}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 f}{12} > \frac{6}{12}$

Divide $f$ by $1$ .

$f > \frac{6}{12}$

Simplify the right side.

Cancel the common factor of $6$ and $12$ .

Factor $6$ out of $6$ .

$f > \frac{6 (1)}{12}$

Cancel the common factors.

Factor $6$ out of $12$ .

$f > \frac{6 \cdot 1}{6 \cdot 2}$

Cancel the common factor.

$f > \frac{6 \cdot 1}{6 \cdot 2}$

Rewrite the expression.

$f > \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$f > \frac{1}{2}$

Interval Notation:

$(\frac{1}{2}, \infty)$