Algebra Examples

$\frac{2}{3} d > 8$

Step 1

Multiply each term in $\frac{2}{3} d > 8$ by $\frac{3}{2}$ .

$\frac{2}{3} d \frac{3}{2} > 8 (\frac{3}{2})$

Step 2

Simplify the left side.

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Step 2.1

Combine $\frac{2}{3}$ and $d$ .

$\frac{2 d}{3} \cdot \frac{3}{2} > 8 (\frac{3}{2})$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $2 d$ .

$\frac{2 (d)}{3} \cdot \frac{3}{2} > 8 (\frac{3}{2})$

Step 2.2.2

Cancel the common factor.

$\frac{2 d}{3} \cdot \frac{3}{2} > 8 (\frac{3}{2})$

Step 2.2.3

Rewrite the expression.

$\frac{d}{3} \cdot 3 > 8 (\frac{3}{2})$

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Cancel the common factor.

$\frac{d}{3} \cdot 3 > 8 (\frac{3}{2})$

Step 2.3.2

Rewrite the expression.

$d > 8 (\frac{3}{2})$

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $8$ .

$d > 2 (4) \frac{3}{2}$

Step 3.1.2

Cancel the common factor.

$d > 2 \cdot 4 \frac{3}{2}$

Step 3.1.3

Rewrite the expression.

$d > 4 \cdot 3$

Step 3.2

Multiply $4$ by $3$ .

$d > 12$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$d > 12$

Interval Notation:

$(12, \infty)$