Algebra Examples

$1 > x - 7$ or $3 < x - 7$

Step 1

Simplify the first inequality.

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Step 1.1

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

$x - 7 < 1$ or $3 < x - 7$

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 $7$ to both sides of the inequality.

$x < 1 + 7$ or $3 < x - 7$

Step 1.2.2

Add $1$ and $7$ .

$x < 8$ or $3 < x - 7$

Step 2

Simplify the second inequality.

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Step 2.1

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

$x < 8$ or $x - 7 > 3$

Step 2.2

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

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Step 2.2.1

Add $7$ to both sides of the inequality.

$x < 8$ or $x > 3 + 7$

Step 2.2.2

Add $3$ and $7$ .

$x < 8$ or $x > 10$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < 8 or x > 10$

Interval Notation:

$(- \infty, 8) \cup (10, \infty)$

Step 4