Algebra Examples

$4 x - 6 < 10$ or $30 < 4 x - 6$

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

Add $6$ to both sides of the inequality.

$4 x < 10 + 6$ or $30 < 4 x - 6$

Step 1.1.2

Add $10$ and $6$ .

$4 x < 16$ or $30 < 4 x - 6$

Step 1.2

Divide each term in $4 x < 16$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 x < 16$ by $4$ .

$\frac{4 x}{4} < \frac{16}{4}$ or $30 < 4 x - 6$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} < \frac{16}{4}$ or $30 < 4 x - 6$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{16}{4}$ or $30 < 4 x - 6$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $16$ by $4$ .

$x < 4$ or $30 < 4 x - 6$

Step 2

Simplify the second inequality.

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Step 2.1

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

$x < 4$ or $4 x - 6 > 30$

Step 2.2

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

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Step 2.2.1

Add $6$ to both sides of the inequality.

$x < 4$ or $4 x > 30 + 6$

Step 2.2.2

Add $30$ and $6$ .

$x < 4$ or $4 x > 36$

Step 2.3

Divide each term in $4 x > 36$ by $4$ and simplify.

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Step 2.3.1

Divide each term in $4 x > 36$ by $4$ .

$x < 4$ or $\frac{4 x}{4} > \frac{36}{4}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $4$ .

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Step 2.3.2.1.1

Cancel the common factor.

$x < 4$ or $\frac{4 x}{4} > \frac{36}{4}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x < 4$ or $x > \frac{36}{4}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $36$ by $4$ .

$x < 4$ or $x > 9$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < 4 or x > 9$

Interval Notation:

$(- \infty, 4) \cup (9, \infty)$

Step 4