Basic Math Examples

$- \frac{x}{6} \leq 3$

Step 1

Divide each term in $- \frac{x}{6} \leq 3$ by $- 1$ and simplify.

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Step 1.1

Divide each term in $- \frac{x}{6} \leq 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{x}{6}}{- 1} \geq \frac{3}{- 1}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{x}{6}}{1} \geq \frac{3}{- 1}$

Step 1.2.2

Divide $\frac{x}{6}$ by $1$ .

$\frac{x}{6} \geq \frac{3}{- 1}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $3$ by $- 1$ .

$\frac{x}{6} \geq - 3$

Step 2

Multiply both sides by $6$ .

$\frac{x}{6} \cdot 6 \geq - 3 \cdot 6$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{x}{6} \cdot 6 \geq - 3 \cdot 6$

Step 3.1.1.2

Rewrite the expression.

$x \geq - 3 \cdot 6$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 3$ by $6$ .

$x \geq - 18$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 18$

Interval Notation:

$[- 18, \infty)$