Pre-Algebra Examples

$- 4 x < 18$

Step 1

Divide each term in $- 4 x < 18$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} > \frac{18}{- 4}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $- 4$ .

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Step 2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} > \frac{18}{- 4}$

Step 2.1.2

Divide $x$ by $1$ .

$x > \frac{18}{- 4}$

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $18$ and $- 4$ .

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Step 3.1.1

Factor $2$ out of $18$ .

$x > \frac{2 (9)}{- 4}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $2$ out of $- 4$ .

$x > \frac{2 \cdot 9}{2 \cdot - 2}$

Step 3.1.2.2

Cancel the common factor.

$x > \frac{2 \cdot 9}{2 \cdot - 2}$

Step 3.1.2.3

Rewrite the expression.

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

Step 3.2

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(- \frac{9}{2}, \infty)$