Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Multiply $10$ by $- 5$ .

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

Step 1.1.3

Multiply $- 5$ by $- 3$ .

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

Step 1.2

Add $- 9$ and $15$ .

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

Step 2

Add $- 6$ and $8$ .

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

$- 53 g + 6 \leq 2$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $6$ from both sides of the inequality.

$- 53 g \leq 2 - 6$

Step 4.2

Subtract $6$ from $2$ .

$- 53 g \leq - 4$

Step 5

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

Tap for more steps...

Step 5.1

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.

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

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $- 53$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $g$ by $1$ .

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

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Dividing two negative values results in a positive value.

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

Step 6

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

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