Algebra Examples

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

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Multiply $2$ by $3$ .

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Move the leading negative in $- \frac{x}{3}$ into the numerator.

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

Step 2.2.1.2

Cancel the common factor.

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

Step 2.2.1.3

Rewrite the expression.

$6 < - x$

Step 3

Solve for $x$ .

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Step 3.1

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

$- x > 6$

Step 3.2

Divide each term in $- x > 6$ by $- 1$ and simplify.

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Step 3.2.1

Divide each term in $- x > 6$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{6}{- 1}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{6}{- 1}$

Step 3.2.2.2

Divide $x$ by $1$ .

$x < \frac{6}{- 1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $6$ by $- 1$ .

$x < - 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - 6$

Interval Notation:

$(- \infty, - 6)$