Algebra Examples

$5 x \geq 20$ or $x + 14 < 16$

Step 1

Divide each term in $5 x \geq 20$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 x \geq 20$ by $5$ .

$\frac{5 x}{5} \geq \frac{20}{5}$ or $x + 14 < 16$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{20}{5}$ or $x + 14 < 16$

Step 1.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{20}{5}$ or $x + 14 < 16$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $20$ by $5$ .

$x \geq 4$ or $x + 14 < 16$

Step 2

Move all terms not containing $x$ to the right side of the inequality.

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Step 2.1

Subtract $14$ from both sides of the inequality.

$x \geq 4$ or $x < 16 - 14$

Step 2.2

Subtract $14$ from $16$ .

$x \geq 4$ or $x < 2$

Step 3

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

$x < 2$ or $x \geq 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 2 or x \geq 4$

Interval Notation:

$(- \infty, 2) \cup [4, \infty)$

Step 5