Solve the Inequality for x 2<-x/3

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

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

Simplify the left side.

Multiply $2$ by $3$ .

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

Simplify the right side.

Cancel the common factor of $3$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

$6 < - x$

Step 3

Solve for $x$ .

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

$- x > 6$

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

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.

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $6$ by $- 1$ .

$x < - 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - 6$

Interval Notation:

$(- \infty, - 6)$

Solve the Inequality for x 2<-x/3

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