Algebra Examples

$9 x \leq - 27$ or $4 x \geq 36$

Step 1

Divide each term in $9 x \leq - 27$ by $9$ and simplify.

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Step 1.1

Divide each term in $9 x \leq - 27$ by $9$ .

$\frac{9 x}{9} \leq \frac{- 27}{9}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $9$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{9 x}{9} \leq \frac{- 27}{9}$

Step 1.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{- 27}{9}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $- 27$ by $9$ .

$x \leq - 3$

Step 2

Divide each term in $4 x \geq 36$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 x \geq 36$ by $4$ .

$\frac{4 x}{4} \geq \frac{36}{4}$

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.

$\frac{4 x}{4} \geq \frac{36}{4}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{36}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $36$ by $4$ .

$x \geq 9$

Step 3

The union consists of all of the elements that are contained in each interval.

$x \leq - 3$ or $x \geq 9$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 3 or x \geq 9$

Interval Notation:

$(- \infty, - 3] \cup [9, \infty)$

Step 5