Solve the Inequality for x 5-3/2x>=1/3

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

Simplify each term.

Combine $x$ and $\frac{3}{2}$ .

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

Move $3$ to the left of $x$ .

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

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

Subtract $5$ from both sides of the inequality.

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

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

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

Combine $- 5$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 5$ by $3$ .

$- \frac{3 x}{2} \geq \frac{1 - 15}{3}$

Subtract $15$ from $1$ .

$- \frac{3 x}{2} \geq \frac{- 14}{3}$

Move the negative in front of the fraction.

$- \frac{3 x}{2} \geq - \frac{14}{3}$

Divide each term in $- \frac{3 x}{2} \geq - \frac{14}{3}$ by $- 1$ and simplify.

Divide each term in $- \frac{3 x}{2} \geq - \frac{14}{3}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{3 x}{2}}{- 1} \leq \frac{- \frac{14}{3}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{3 x}{2}}{1} \leq \frac{- \frac{14}{3}}{- 1}$

Divide $\frac{3 x}{2}$ by $1$ .

$\frac{3 x}{2} \leq \frac{- \frac{14}{3}}{- 1}$

Simplify the right side.

Dividing two negative values results in a positive value.

$\frac{3 x}{2} \leq \frac{\frac{14}{3}}{1}$

Divide $\frac{14}{3}$ by $1$ .

$\frac{3 x}{2} \leq \frac{14}{3}$

Multiply both sides by $2$ .

$\frac{3 x}{2} \cdot 2 \leq \frac{14}{3} \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 x}{2} \cdot 2 \leq \frac{14}{3} \cdot 2$

Rewrite the expression.

$3 x \leq \frac{14}{3} \cdot 2$

Simplify the right side.

Multiply $\frac{14}{3} \cdot 2$ .

Combine $\frac{14}{3}$ and $2$ .

$3 x \leq \frac{14 \cdot 2}{3}$

Multiply $14$ by $2$ .

$3 x \leq \frac{28}{3}$

Divide each term in $3 x \leq \frac{28}{3}$ by $3$ and simplify.

Divide each term in $3 x \leq \frac{28}{3}$ by $3$ .

$\frac{3 x}{3} \leq \frac{\frac{28}{3}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{\frac{28}{3}}{3}$

Divide $x$ by $1$ .

$x \leq \frac{\frac{28}{3}}{3}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x \leq \frac{28}{3} \cdot \frac{1}{3}$

Multiply $\frac{28}{3} \cdot \frac{1}{3}$ .

Multiply $\frac{28}{3}$ by $\frac{1}{3}$ .

$x \leq \frac{28}{3 \cdot 3}$

Multiply $3$ by $3$ .

$x \leq \frac{28}{9}$

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{28}{9}$

Interval Notation:

$(- \infty, \frac{28}{9}]$

Solve the Inequality for x 5-3/2x>=1/3

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