Algebra Examples

$2 x + 1 > 9$ or $x - 4 < 6$

Step 1

Simplify the first inequality.

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Step 1.1

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

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Step 1.1.1

Subtract $1$ from both sides of the inequality.

$2 x > 9 - 1$ or $x - 4 < 6$

Step 1.1.2

Subtract $1$ from $9$ .

$2 x > 8$ or $x - 4 < 6$

Step 1.2

Divide each term in $2 x > 8$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 x > 8$ by $2$ .

$\frac{2 x}{2} > \frac{8}{2}$ or $x - 4 < 6$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} > \frac{8}{2}$ or $x - 4 < 6$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{8}{2}$ or $x - 4 < 6$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $8$ by $2$ .

$x > 4$ or $x - 4 < 6$

Step 2

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

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Step 2.1

Add $4$ to both sides of the inequality.

$x > 4$ or $x < 6 + 4$

Step 2.2

Add $6$ and $4$ .

$x > 4$ or $x < 10$

Step 3

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

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Step 5