Algebra Examples

$5 < x - 1$ or $x - 1 > 9$

Step 1

Simplify the first inequality.

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Step 1.1

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

$x - 1 > 5$ or $x - 1 > 9$

Step 1.2

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

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Step 1.2.1

Add $1$ to both sides of the inequality.

$x > 5 + 1$ or $x - 1 > 9$

Step 1.2.2

Add $5$ and $1$ .

$x > 6$ or $x - 1 > 9$

Step 2

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

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Step 2.1

Add $1$ to both sides of the inequality.

$x > 6$ or $x > 9 + 1$

Step 2.2

Add $9$ and $1$ .

$x > 6$ or $x > 10$

Step 3

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

$x > 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 6$

Interval Notation:

$(6, \infty)$

Step 5