Solve for x -2x>1/9

$- 2 x > \frac{1}{9}$

Step 1

Divide each term in $- 2 x > \frac{1}{9}$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{\frac{1}{9}}{- 2}$

Step 2

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{\frac{1}{9}}{- 2}$

Divide $x$ by $1$ .

$x < \frac{\frac{1}{9}}{- 2}$

Step 3

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x < \frac{1}{9} \cdot \frac{1}{- 2}$

Move the negative in front of the fraction.

$x < \frac{1}{9} (- \frac{1}{2})$

Multiply $\frac{1}{9} (- \frac{1}{2})$ .

Multiply $\frac{1}{9}$ by $\frac{1}{2}$ .

$x < - \frac{1}{9 \cdot 2}$

Multiply $9$ by $2$ .

$x < - \frac{1}{18}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{1}{18}$

Interval Notation:

$(- \infty, - \frac{1}{18})$

Solve for x -2x>1/9

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