Solve the Inequality for f -7f-5(-8f+10)<-4f-3-3

$- 7 f - 5 (- 8 f + 10) < - 4 f - 3 - 3$

Simplify $- 7 f - 5 (- 8 f + 10)$ .

Simplify each term.

Apply the distributive property.

$- 7 f - 5 (- 8 f) - 5 \cdot 10 < - 4 f - 3 - 3$

Multiply $- 8$ by $- 5$ .

$- 7 f + 40 f - 5 \cdot 10 < - 4 f - 3 - 3$

Multiply $- 5$ by $10$ .

$- 7 f + 40 f - 50 < - 4 f - 3 - 3$

Add $- 7 f$ and $40 f$ .

$33 f - 50 < - 4 f - 3 - 3$

Subtract $3$ from $- 3$ .

$33 f - 50 < - 4 f - 6$

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

Add $4 f$ to both sides of the inequality.

$33 f - 50 + 4 f < - 6$

Add $33 f$ and $4 f$ .

$37 f - 50 < - 6$

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

Add $50$ to both sides of the inequality.

$37 f < - 6 + 50$

Add $- 6$ and $50$ .

$37 f < 44$

Divide each term in $37 f < 44$ by $37$ and simplify.

Divide each term in $37 f < 44$ by $37$ .

$\frac{37 f}{37} < \frac{44}{37}$

Simplify the left side.

Cancel the common factor of $37$ .

Cancel the common factor.

$\frac{37 f}{37} < \frac{44}{37}$

Divide $f$ by $1$ .

$f < \frac{44}{37}$

The result can be shown in multiple forms.

Inequality Form:

$f < \frac{44}{37}$

Interval Notation:

$(- \infty, \frac{44}{37})$