Algebra Examples

$3 x < 21$ or $5 x > 55$

Step 1

Divide each term in $3 x < 21$ by $3$ and simplify.

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Step 1.1

Divide each term in $3 x < 21$ by $3$ .

$\frac{3 x}{3} < \frac{21}{3}$ or $5 x > 55$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $3$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{3 x}{3} < \frac{21}{3}$ or $5 x > 55$

Step 1.2.1.2

Divide $x$ by $1$ .

$x < \frac{21}{3}$ or $5 x > 55$

$x < \frac{21}{3}$ or $5 x > 55$

$x < \frac{21}{3}$ or $5 x > 55$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $21$ by $3$ .

$x < 7$ or $5 x > 55$

$x < 7$ or $5 x > 55$

$x < 7$ or $5 x > 55$

Step 2

Divide each term in $5 x > 55$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 x > 55$ by $5$ .

$x < 7$ or $\frac{5 x}{5} > \frac{55}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$x < 7$ or $\frac{5 x}{5} > \frac{55}{5}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x < 7$ or $x > \frac{55}{5}$

$x < 7$ or $x > \frac{55}{5}$

$x < 7$ or $x > \frac{55}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $55$ by $5$ .

$x < 7$ or $x > 11$

$x < 7$ or $x > 11$

$x < 7$ or $x > 11$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < 7 or x > 11$

Interval Notation:

$(- \infty, 7) \cup (11, \infty)$

Step 4

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