Solve the Inequality for f -10f+1>-f-5

$- 10 f + 1 > - f - 5$

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

Add $f$ to both sides of the inequality.

$- 10 f + 1 + f > - 5$

Add $- 10 f$ and $f$ .

$- 9 f + 1 > - 5$

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

Subtract $1$ from both sides of the inequality.

$- 9 f > - 5 - 1$

Subtract $1$ from $- 5$ .

$- 9 f > - 6$

Divide each term in $- 9 f > - 6$ by $- 9$ and simplify.

Divide each term in $- 9 f > - 6$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 f}{- 9} < \frac{- 6}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 f}{- 9} < \frac{- 6}{- 9}$

Divide $f$ by $1$ .

$f < \frac{- 6}{- 9}$

Simplify the right side.

Cancel the common factor of $- 6$ and $- 9$ .

Factor $- 3$ out of $- 6$ .

$f < \frac{- 3 (2)}{- 9}$

Cancel the common factors.

Factor $- 3$ out of $- 9$ .

$f < \frac{- 3 \cdot 2}{- 3 \cdot 3}$

Cancel the common factor.

$f < \frac{- 3 \cdot 2}{- 3 \cdot 3}$

Rewrite the expression.

$f < \frac{2}{3}$

The result can be shown in multiple forms.

Inequality Form:

$f < \frac{2}{3}$

Interval Notation:

$(- \infty, \frac{2}{3})$

Solve the Inequality for f -10f+1>-f-5

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