Solve for g -9-5(10g-3)<=3g-6+8

$- 9 - 5 (10 g - 3) \leq 3 g - 6 + 8$

Simplify $- 9 - 5 (10 g - 3)$ .

Simplify each term.

Apply the distributive property.

$- 9 - 5 (10 g) - 5 \cdot - 3 \leq 3 g - 6 + 8$

Multiply $10$ by $- 5$ .

$- 9 - 50 g - 5 \cdot - 3 \leq 3 g - 6 + 8$

Multiply $- 5$ by $- 3$ .

$- 9 - 50 g + 15 \leq 3 g - 6 + 8$

Add $- 9$ and $15$ .

$- 50 g + 6 \leq 3 g - 6 + 8$

Add $- 6$ and $8$ .

$- 50 g + 6 \leq 3 g + 2$

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

Subtract $3 g$ from both sides of the inequality.

$- 50 g + 6 - 3 g \leq 2$

Subtract $3 g$ from $- 50 g$ .

$- 53 g + 6 \leq 2$

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

Subtract $6$ from both sides of the inequality.

$- 53 g \leq 2 - 6$

Subtract $6$ from $2$ .

$- 53 g \leq - 4$

Divide each term in $- 53 g \leq - 4$ by $- 53$ and simplify.

Divide each term in $- 53 g \leq - 4$ by $- 53$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 53 g}{- 53} \geq \frac{- 4}{- 53}$

Simplify the left side.

Cancel the common factor of $- 53$ .

Cancel the common factor.

$\frac{- 53 g}{- 53} \geq \frac{- 4}{- 53}$

Divide $g$ by $1$ .

$g \geq \frac{- 4}{- 53}$

Simplify the right side.

Dividing two negative values results in a positive value.

$g \geq \frac{4}{53}$

The result can be shown in multiple forms.

Inequality Form:

$g \geq \frac{4}{53}$

Interval Notation:

$[\frac{4}{53}, \infty)$

Solve for g -9-5(10g-3)<=3g-6+8

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