Solve the Inequality for x -2/3<-4x

$- \frac{2}{3} < - 4 x$

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

$- 4 x > - \frac{2}{3}$

Divide each term in $- 4 x > - \frac{2}{3}$ by $- 4$ and simplify.

Divide each term in $- 4 x > - \frac{2}{3}$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} < \frac{- \frac{2}{3}}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} < \frac{- \frac{2}{3}}{- 4}$

Divide $x$ by $1$ .

$x < \frac{- \frac{2}{3}}{- 4}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x < - \frac{2}{3} \cdot \frac{1}{- 4}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$x < \frac{- 2}{3} \cdot \frac{1}{- 4}$

Factor $2$ out of $- 2$ .

$x < \frac{2 (- 1)}{3} \cdot \frac{1}{- 4}$

Factor $2$ out of $- 4$ .

$x < \frac{2 \cdot - 1}{3} \cdot \frac{1}{2 \cdot - 2}$

Cancel the common factor.

$x < \frac{2 \cdot - 1}{3} \cdot \frac{1}{2 \cdot - 2}$

Rewrite the expression.

$x < \frac{- 1}{3} \cdot \frac{1}{- 2}$

Multiply $\frac{- 1}{3}$ by $\frac{1}{- 2}$ .

$x < \frac{- 1}{3 \cdot - 2}$

Multiply $3$ by $- 2$ .

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

Dividing two negative values results in a positive value.

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

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(- \infty, \frac{1}{6})$

Solve the Inequality for x -2/3<-4x

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