Solve the Inequality for x 2/3-1/2x>-1/3

$\frac{2}{3} - \frac{1}{2} x > - \frac{1}{3}$

Combine $x$ and $\frac{1}{2}$ .

$\frac{2}{3} - \frac{x}{2} > - \frac{1}{3}$

Move all terms not containing $x$ to the right side of the inequality.

Subtract $\frac{2}{3}$ from both sides of the inequality.

$- \frac{x}{2} > - \frac{1}{3} - \frac{2}{3}$

Combine the numerators over the common denominator.

$- \frac{x}{2} > \frac{- 1 - 2}{3}$

Subtract $2$ from $- 1$ .

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

Divide $- 3$ by $3$ .

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

Divide each term in $- \frac{x}{2} > - 1$ by $- 1$ and simplify.

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $\frac{x}{2}$ by $1$ .

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

Simplify the right side.

Divide $- 1$ by $- 1$ .

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

Multiply both sides by $2$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$x < 1 \cdot 2$

Simplify the right side.

Multiply $2$ by $1$ .

$x < 2$

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$

Solve the Inequality for x 2/3-1/2x>-1/3

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