Finite Math Examples

$x < - 4 x > 6$

Step 1

Divide each term in the inequality by $- 4$ .

$\frac{x}{- 4} > \frac{- 4 x}{- 4} < \frac{6}{- 4}$

Step 2

Move the negative in front of the fraction.

$- \frac{x}{4} > \frac{- 4 x}{- 4} < \frac{6}{- 4}$

Step 3

Cancel the common factor of $- 4$ .

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Step 3.1

Cancel the common factor.

$- \frac{x}{4} > \frac{- 4 x}{- 4} < \frac{6}{- 4}$

Step 3.2

Divide $x$ by $1$ .

$- \frac{x}{4} > x < \frac{6}{- 4}$

Step 4

Cancel the common factor of $6$ and $- 4$ .

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Step 4.1

Factor $2$ out of $6$ .

$- \frac{x}{4} > x < \frac{2 (3)}{- 4}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $- 4$ .

$- \frac{x}{4} > x < \frac{2 \cdot 3}{2 \cdot - 2}$

Step 4.2.2

Cancel the common factor.

$- \frac{x}{4} > x < \frac{2 \cdot 3}{2 \cdot - 2}$

Step 4.2.3

Rewrite the expression.

$- \frac{x}{4} > x < \frac{3}{- 2}$

Step 5

Move the negative in front of the fraction.

$- \frac{x}{4} > x < - \frac{3}{2}$

Step 6

Convert the inequality to interval notation.

$(- \frac{x}{4}, - \frac{3}{2})$

Step 7