Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Subtract $2$ from $- 1$ .

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

Step 2.4

Divide $- 3$ by $3$ .

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

Step 3

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

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Step 3.1

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.

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

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

Step 3.2.2

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

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 1$ by $- 1$ .

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

Step 4

Multiply both sides by $2$ .

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

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1

Cancel the common factor.

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

Step 5.1.1.2

Rewrite the expression.

$x < 1 \cdot 2$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $2$ by $1$ .

$x < 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$