Solve for x -1/2x+1/3>3/5

$- \frac{1}{2} x + \frac{1}{3} > \frac{3}{5}$

Step 1

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

$- \frac{x}{2} + \frac{1}{3} > \frac{3}{5}$

Step 2

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

Subtract $\frac{1}{3}$ from both sides of the inequality.

$- \frac{x}{2} > \frac{3}{5} - \frac{1}{3}$

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{x}{2} > \frac{3}{5} \cdot \frac{3}{3} - \frac{1}{3}$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{x}{2} > \frac{3}{5} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{5}{5}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{5}$ by $\frac{3}{3}$ .

$- \frac{x}{2} > \frac{3 \cdot 3}{5 \cdot 3} - \frac{1}{3} \cdot \frac{5}{5}$

Multiply $5$ by $3$ .

$- \frac{x}{2} > \frac{3 \cdot 3}{15} - \frac{1}{3} \cdot \frac{5}{5}$

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$- \frac{x}{2} > \frac{3 \cdot 3}{15} - \frac{5}{3 \cdot 5}$

Multiply $3$ by $5$ .

$- \frac{x}{2} > \frac{3 \cdot 3}{15} - \frac{5}{15}$

Combine the numerators over the common denominator.

$- \frac{x}{2} > \frac{3 \cdot 3 - 5}{15}$

Simplify the numerator.

Multiply $3$ by $3$ .

$- \frac{x}{2} > \frac{9 - 5}{15}$

Subtract $5$ from $9$ .

$- \frac{x}{2} > \frac{4}{15}$

Step 3

Divide each term in $- \frac{x}{2} > \frac{4}{15}$ by $- 1$ and simplify.

Divide each term in $- \frac{x}{2} > \frac{4}{15}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{x}{2}}{- 1} < \frac{\frac{4}{15}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{x}{2}}{1} < \frac{\frac{4}{15}}{- 1}$

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

$\frac{x}{2} < \frac{\frac{4}{15}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{\frac{4}{15}}{- 1}$ .

$\frac{x}{2} < - 1 \cdot \frac{4}{15}$

Rewrite $- 1 \cdot \frac{4}{15}$ as $- \frac{4}{15}$ .

$\frac{x}{2} < - \frac{4}{15}$

Step 4

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 < - \frac{4}{15} \cdot 2$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x}{2} \cdot 2 < - \frac{4}{15} \cdot 2$

Rewrite the expression.

$x < - \frac{4}{15} \cdot 2$

Simplify the right side.

Simplify $- \frac{4}{15} \cdot 2$ .

Multiply $- \frac{4}{15} \cdot 2$ .

Multiply $2$ by $- 1$ .

$x < - 2 (\frac{4}{15})$

Combine $- 2$ and $\frac{4}{15}$ .

$x < \frac{- 2 \cdot 4}{15}$

Multiply $- 2$ by $4$ .

$x < \frac{- 8}{15}$

Move the negative in front of the fraction.

$x < - \frac{8}{15}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{8}{15}$

Interval Notation:

$(- \infty, - \frac{8}{15})$

Solve for x -1/2x+1/3>3/5

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