Algebra Examples

$g (x) < - \sqrt{x - 3} + 2$

Step 1

Divide each term in $g x < - \sqrt{x - 3} + 2$ by $x$ .

$\frac{g x}{x} < \frac{- \sqrt{x - 3}}{x} + \frac{2}{x}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $x$ .

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Step 2.1.1

Cancel the common factor.

$\frac{g x}{x} < \frac{- \sqrt{x - 3}}{x} + \frac{2}{x}$

Step 2.1.2

Divide $g$ by $1$ .

$g < \frac{- \sqrt{x - 3}}{x} + \frac{2}{x}$

Step 3

Simplify the right side.

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Step 3.1

Combine the numerators over the common denominator.

$g < \frac{- \sqrt{x - 3} + 2}{x}$

Step 3.2

Factor $- 1$ out of $- \sqrt{x - 3}$ .

$g < \frac{- (\sqrt{x - 3}) + 2}{x}$

Step 3.3

Rewrite $2$ as $- 1 (- 2)$ .

$g < \frac{- (\sqrt{x - 3}) - 1 (- 2)}{x}$

Step 3.4

Factor $- 1$ out of $- (\sqrt{x - 3}) - 1 (- 2)$ .

$g < \frac{- (\sqrt{x - 3} - 2)}{x}$

Step 3.5

Simplify the expression.

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Step 3.5.1

Rewrite $- (\sqrt{x - 3} - 2)$ as $- 1 (\sqrt{x - 3} - 2)$ .

$g < \frac{- 1 (\sqrt{x - 3} - 2)}{x}$

Step 3.5.2

Move the negative in front of the fraction.

$g < - \frac{\sqrt{x - 3} - 2}{x}$

Step 4