Solve the Inequality for f 9f-2(3f+5)<=8

$9 f - 2 (3 f + 5) \leq 8$

Step 1

Simplify $9 f - 2 (3 f + 5)$ .

Simplify each term.

Apply the distributive property.

$9 f - 2 (3 f) - 2 \cdot 5 \leq 8$

Multiply $3$ by $- 2$ .

$9 f - 6 f - 2 \cdot 5 \leq 8$

Multiply $- 2$ by $5$ .

$9 f - 6 f - 10 \leq 8$

Subtract $6 f$ from $9 f$ .

$3 f - 10 \leq 8$

Step 2

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

Add $10$ to both sides of the inequality.

$3 f \leq 8 + 10$

Add $8$ and $10$ .

$3 f \leq 18$

Step 3

Divide each term in $3 f \leq 18$ by $3$ and simplify.

Divide each term in $3 f \leq 18$ by $3$ .

$\frac{3 f}{3} \leq \frac{18}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 f}{3} \leq \frac{18}{3}$

Divide $f$ by $1$ .

$f \leq \frac{18}{3}$

Simplify the right side.

Divide $18$ by $3$ .

$f \leq 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$f \leq 6$

Interval Notation:

$(- \infty, 6]$