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.

$x > - 1 + 3$ and $x - 2 > 4$

Add $- 1$ and $3$ .

$x > 2$ 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 $x > 2 + 4$

Add $2$ and $4$ .

$x > 2$ and $x > 6$

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

$x > 6$

interval notation: $(6, \infty)$

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