Algebra Examples

$x^{2} - 4 n x + 4 m > 0$

Step 1

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

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Step 1.1

Subtract $x^{2}$ from both sides of the inequality.

$- 4 n x + 4 m > - x^{2}$

Step 1.2

Add $4 n x$ to both sides of the inequality.

$4 m > - x^{2} + 4 n x$

Step 2

Divide each term in $4 m > - x^{2} + 4 n x$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 m > - x^{2} + 4 n x$ by $4$ .

$\frac{4 m}{4} > \frac{- x^{2}}{4} + \frac{4 n x}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 m}{4} > \frac{- x^{2}}{4} + \frac{4 n x}{4}$

Step 2.2.1.2

Divide $m$ by $1$ .

$m > \frac{- x^{2}}{4} + \frac{4 n x}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Move the negative in front of the fraction.

$m > - \frac{x^{2}}{4} + \frac{4 n x}{4}$

Step 2.3.1.2

Cancel the common factor of $4$ .

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Step 2.3.1.2.1

Cancel the common factor.

$m > - \frac{x^{2}}{4} + \frac{4 n x}{4}$

Step 2.3.1.2.2

Divide $n x$ by $1$ .

$m > - \frac{x^{2}}{4} + n x$