Precalculus Examples

$x \geq 1$ , $x - 1 < 7$

Step 1

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

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Add $1$ to both sides of the inequality.

$x \geq 1$ and $x < 7 + 1$

Add $7$ and $1$ .

$x \geq 1$ and $x < 8$

Step 2

The intersection consists of the elements that are contained in both intervals.

$1 \leq x < 8$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x < 8$

Interval Notation:

$[1, 8)$

Step 4