Algebra Examples

$x - 2 < 6$ or $\frac{x}{3} > 4$

Step 1

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

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Step 1.1

Add $2$ to both sides of the inequality.

$x < 6 + 2$ or $\frac{x}{3} > 4$

Step 1.2

Add $6$ and $2$ .

$x < 8$ or $\frac{x}{3} > 4$

$x < 8$ or $\frac{x}{3} > 4$

Step 2

Simplify the second inequality.

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Step 2.1

Multiply both sides by $3$ .

$x < 8$ or $\frac{x}{3} \cdot 3 > 4 \cdot 3$

Step 2.2

Simplify.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Cancel the common factor.

$x < 8$ or $\frac{x}{3} \cdot 3 > 4 \cdot 3$

Step 2.2.1.1.2

Rewrite the expression.

$x < 8$ or $x > 4 \cdot 3$

$x < 8$ or $x > 4 \cdot 3$

$x < 8$ or $x > 4 \cdot 3$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Multiply $4$ by $3$ .

$x < 8$ or $x > 12$

$x < 8$ or $x > 12$

$x < 8$ or $x > 12$

$x < 8$ or $x > 12$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < 8 or x > 12$

Interval Notation:

$(- \infty, 8) \cup (12, \infty)$

Step 4

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$