Solve the Inequality for f (3f-10)/5>7

$\frac{3 f - 10}{5} > 7$

Step 1

Multiply both sides by $5$ .

$\frac{3 f - 10}{5} \cdot 5 > 7 \cdot 5$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{3 f - 10}{5} \cdot 5 > 7 \cdot 5$

Rewrite the expression.

$3 f - 10 > 7 \cdot 5$

Simplify the right side.

Multiply $7$ by $5$ .

$3 f - 10 > 35$

Step 3

Solve for $f$ .

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

Add $10$ to both sides of the inequality.

$3 f > 35 + 10$

Add $35$ and $10$ .

$3 f > 45$

Divide each term in $3 f > 45$ by $3$ and simplify.

Divide each term in $3 f > 45$ by $3$ .

$\frac{3 f}{3} > \frac{45}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 f}{3} > \frac{45}{3}$

Divide $f$ by $1$ .

$f > \frac{45}{3}$

Simplify the right side.

Divide $45$ by $3$ .

$f > 15$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$f > 15$

Interval Notation:

$(15, \infty)$