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.

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

Subtract $1$ from $3$ .

$x < 2$ and $x - 2 < 4$

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.

$x < 2$ and $x < 4 + 2$

Add $4$ and $2$ .

$x < 2$ and $x < 6$

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

$x < 2$

Interval Notation: $(- \infty, 2)$

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