Solve for f -f-9>=2f-1

$- f - 9 \geq 2 f - 1$

Step 1

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

Subtract $2 f$ from both sides of the inequality.

$- f - 9 - 2 f \geq - 1$

Subtract $2 f$ from $- f$ .

$- 3 f - 9 \geq - 1$

Step 2

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

Add $9$ to both sides of the inequality.

$- 3 f \geq - 1 + 9$

Add $- 1$ and $9$ .

$- 3 f \geq 8$

Step 3

Divide each term in $- 3 f \geq 8$ by $- 3$ and simplify.

Divide each term in $- 3 f \geq 8$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 f}{- 3} \leq \frac{8}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 f}{- 3} \leq \frac{8}{- 3}$

Divide $f$ by $1$ .

$f \leq \frac{8}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$f \leq - \frac{8}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$f \leq - \frac{8}{3}$

Interval Notation:

$(- \infty, - \frac{8}{3}]$

Solve for f -f-9>=2f-1

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