Precalculus Examples

x + 1 < 3

$x + 1 < 3$ ,

x - 2 < 4

$x - 2 < 4$

Step 1

Move all terms not containing

x

$x$ to the right side of the inequality.

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Step 1.1

Subtract

1

$1$ from both sides of the inequality.

x < 3 - 1

$x < 3 - 1$ or

x - 2 < 4

$x - 2 < 4$

Step 1.2

Subtract

1

$1$ from

3

$3$ .

x < 2

$x < 2$ or

x - 2 < 4

$x - 2 < 4$

x < 2

$x < 2$ or

x - 2 < 4

$x - 2 < 4$

Step 2

Move all terms not containing

x

$x$ to the right side of the inequality.

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Step 2.1

Add

2

$2$ to both sides of the inequality.

x < 2

$x < 2$ or

x < 4 + 2

$x < 4 + 2$

Step 2.2

Add

4

$4$ and

2

$2$ .

x < 2

$x < 2$ or

x < 6

$x < 6$

x < 2

$x < 2$ or

x < 6

$x < 6$

Step 3

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

x < 6

$x < 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

x < 6

$x < 6$

Interval Notation:

(- \infty, 6)

$(- \infty, 6)$

Step 5

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