Algebra Examples

$3 x \geq - 12$ and $8 x \leq 16$

Step 1

Divide each term in $3 x \geq - 12$ by $3$ and simplify.

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Step 1.1

Divide each term in $3 x \geq - 12$ by $3$ .

$\frac{3 x}{3} \geq \frac{- 12}{3}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $3$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{- 12}{3}$

Step 1.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 12}{3}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $- 12$ by $3$ .

$x \geq - 4$

Step 2

Divide each term in $8 x \leq 16$ by $8$ and simplify.

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Step 2.1

Divide each term in $8 x \leq 16$ by $8$ .

$\frac{8 x}{8} \leq \frac{16}{8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} \leq \frac{16}{8}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{16}{8}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $16$ by $8$ .

$x \leq 2$

Step 3

The intersection consists of the elements that are contained in both intervals.

$- 4 \leq x \leq 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq x \leq 2$

Interval Notation:

$[- 4, 2]$

Step 5