Pre-Algebra Examples

$10 + \frac{g}{- 9} > 12$

Step 1

Move the negative in front of the fraction.

$10 - \frac{g}{9} > 12$

Step 2

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

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Step 2.1

Subtract $10$ from both sides of the inequality.

$- \frac{g}{9} > 12 - 10$

Step 2.2

Subtract $10$ from $12$ .

$- \frac{g}{9} > 2$

Step 3

Divide each term in $- \frac{g}{9} > 2$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- \frac{g}{9} > 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{g}{9}}{- 1} < \frac{2}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{g}{9}}{1} < \frac{2}{- 1}$

Step 3.2.2

Divide $\frac{g}{9}$ by $1$ .

$\frac{g}{9} < \frac{2}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $2$ by $- 1$ .

$\frac{g}{9} < - 2$

Step 4

Multiply both sides by $9$ .

$\frac{g}{9} \cdot 9 < - 2 \cdot 9$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $9$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{g}{9} \cdot 9 < - 2 \cdot 9$

Step 5.1.1.2

Rewrite the expression.

$g < - 2 \cdot 9$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 2$ by $9$ .

$g < - 18$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$g < - 18$

Interval Notation:

$(- \infty, - 18)$