Precalculus Examples

$x + 1 < 3$ , $x - 2 < 4$

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

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Subtract $1$ from both sides of the inequality.

$x < 3 - 1$ or $x - 2 < 4$

Subtract $1$ from $3$ .

$x < 2$ or $x - 2 < 4$

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

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Add $2$ to both sides of the inequality.

$x < 2$ or $x < 4 + 2$

Add $4$ and $2$ .

$x < 2$ or $x < 6$

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

$x < 6$

The result can be shown in multiple forms.

Inequality Form:

$x < 6$

Interval Notation:

$(- \infty, 6)$

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