Algebra Examples

$2 < 2 x < 6$

Step 1

Solve $2 < 2 x$ for $x$ .

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Step 1.1

Rewrite so $x$ is on the left side of the inequality.

$2 x > 2$

Step 1.2

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

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Step 1.2.1

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

$\frac{2 x}{2} > \frac{2}{2}$

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.

$\frac{2 x}{2} > \frac{2}{2}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{2}{2}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $2$ by $2$ .

$x > 1$

Step 2

Divide each term in $2 x < 6$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 x < 6$ by $2$ .

$\frac{2 x}{2} < \frac{6}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} < \frac{6}{2}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x < \frac{6}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $6$ by $2$ .

$x < 3$

Step 3

Find the intersection of $x > 1$ and $x < 3$ .

$1 < x < 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$1 < x < 3$

Interval Notation:

$(1, 3)$

Step 5