Algebra Examples

$10 < x + 2$ or $x + 2 < 14$

Step 1

Simplify the first inequality.

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Step 1.1

Rewrite so $x$ is on the left side of the inequality.

$x + 2 > 10$ or $x + 2 < 14$

Step 1.2

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

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Step 1.2.1

Subtract $2$ from both sides of the inequality.

$x > 10 - 2$ or $x + 2 < 14$

Step 1.2.2

Subtract $2$ from $10$ .

$x > 8$ or $x + 2 < 14$

Step 2

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

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Step 2.1

Subtract $2$ from both sides of the inequality.

$x > 8$ or $x < 14 - 2$

Step 2.2

Subtract $2$ from $14$ .

$x > 8$ or $x < 12$

Step 3

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

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Step 5