Algebra Examples

$1 \leq x - 7$ or $x - 7 < 4$

Step 1

Simplify the first inequality.

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Step 1.1

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

$x - 7 \geq 1$ or $x - 7 < 4$

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.

$x \geq 1 + 7$ or $x - 7 < 4$

Step 1.2.2

Add $1$ and $7$ .

$x \geq 8$ or $x - 7 < 4$

Step 2

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

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Step 2.1

Add $7$ to both sides of the inequality.

$x \geq 8$ or $x < 4 + 7$

Step 2.2

Add $4$ and $7$ .

$x \geq 8$ or $x < 11$

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