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

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

Rewrite so $s$ is on the left side of the inequality.

$- 4 s + 3 - s > - 10 + 5 (7 s + 8)$

Subtract $s$ from $- 4 s$ .

$- 5 s + 3 > - 10 + 5 (7 s + 8)$

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

Simplify each term.

Apply the distributive property.

$- 5 s + 3 > - 10 + 5 (7 s) + 5 \cdot 8$

Multiply $7$ by $5$ .

$- 5 s + 3 > - 10 + 35 s + 5 \cdot 8$

Multiply $5$ by $8$ .

$- 5 s + 3 > - 10 + 35 s + 40$

Add $- 10$ and $40$ .

$- 5 s + 3 > 35 s + 30$

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

Subtract $35 s$ from both sides of the inequality.

$- 5 s + 3 - 35 s > 30$

Subtract $35 s$ from $- 5 s$ .

$- 40 s + 3 > 30$

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

Subtract $3$ from both sides of the inequality.

$- 40 s > 30 - 3$

Subtract $3$ from $30$ .

$- 40 s > 27$

Divide each term in $- 40 s > 27$ by $- 40$ and simplify.

Divide each term in $- 40 s > 27$ by $- 40$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 40 s}{- 40} < \frac{27}{- 40}$

Simplify the left side.

Cancel the common factor of $- 40$ .

Cancel the common factor.

$\frac{- 40 s}{- 40} < \frac{27}{- 40}$

Divide $s$ by $1$ .

$s < \frac{27}{- 40}$

Simplify the right side.

Move the negative in front of the fraction.

$s < - \frac{27}{40}$

The result can be shown in multiple forms.

Inequality Form:

$s < - \frac{27}{40}$

Interval Notation:

$(- \infty, - \frac{27}{40})$

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

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