Algebra Examples

$- 6 > \frac{2}{3} x$

Step 1

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

$\frac{2}{3} x < - 6$

Step 2

Multiply each term in $\frac{2}{3} x < - 6$ by $\frac{3}{2}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{2}{3} x < - 6$ by $\frac{3}{2}$ .

$\frac{2}{3} x \frac{3}{2} < - 6 (\frac{3}{2})$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

$\frac{2 x}{3} \cdot \frac{3}{2} < - 6 (\frac{3}{2})$

Step 2.2.2

Cancel the common factor of $2$ .

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Step 2.2.2.1

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{3} \cdot \frac{3}{2} < - 6 (\frac{3}{2})$

Step 2.2.2.2

Cancel the common factor.

$\frac{2 x}{3} \cdot \frac{3}{2} < - 6 (\frac{3}{2})$

Step 2.2.2.3

Rewrite the expression.

$\frac{x}{3} \cdot 3 < - 6 (\frac{3}{2})$

Step 2.2.3

Cancel the common factor of $3$ .

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Step 2.2.3.1

Cancel the common factor.

$\frac{x}{3} \cdot 3 < - 6 (\frac{3}{2})$

Step 2.2.3.2

Rewrite the expression.

$x < - 6 (\frac{3}{2})$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $2$ .

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Step 2.3.1.1

Factor $2$ out of $- 6$ .

$x < 2 (- 3) \frac{3}{2}$

Step 2.3.1.2

Cancel the common factor.

$x < 2 \cdot - 3 \frac{3}{2}$

Step 2.3.1.3

Rewrite the expression.

$x < - 3 \cdot 3$

Step 2.3.2

Multiply $- 3$ by $3$ .

$x < - 9$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - 9$

Interval Notation:

$(- \infty, - 9)$