Solve the Inequality for x 3x-5/6>=(-2x)/3

$3 x - \frac{5}{6} \geq \frac{- 2 x}{3}$

Multiply both sides by $3$ .

$(3 x - \frac{5}{6}) \cdot 3 \geq \frac{- 2 x}{3} \cdot 3$

Simplify.

Simplify the left side.

Simplify $(3 x - \frac{5}{6}) \cdot 3$ .

Apply the distributive property.

$3 x \cdot 3 - \frac{5}{6} \cdot 3 \geq \frac{- 2 x}{3} \cdot 3$

Multiply $3$ by $3$ .

$9 x - \frac{5}{6} \cdot 3 \geq \frac{- 2 x}{3} \cdot 3$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$9 x + \frac{- 5}{6} \cdot 3 \geq \frac{- 2 x}{3} \cdot 3$

Factor $3$ out of $6$ .

$9 x + \frac{- 5}{3 (2)} \cdot 3 \geq \frac{- 2 x}{3} \cdot 3$

Cancel the common factor.

$9 x + \frac{- 5}{3 \cdot 2} \cdot 3 \geq \frac{- 2 x}{3} \cdot 3$

Rewrite the expression.

$9 x + \frac{- 5}{2} \geq \frac{- 2 x}{3} \cdot 3$

Move the negative in front of the fraction.

$9 x - \frac{5}{2} \geq \frac{- 2 x}{3} \cdot 3$

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

$9 x - \frac{5}{2} \geq \frac{- 2 x}{3} \cdot 3$

Rewrite the expression.

$9 x - \frac{5}{2} \geq - 2 x$

Solve for $x$ .

Move all terms containing $x$ to the left side of the inequality.

Add $2 x$ to both sides of the inequality.

$9 x - \frac{5}{2} + 2 x \geq 0$

Add $9 x$ and $2 x$ .

$11 x - \frac{5}{2} \geq 0$

Add $\frac{5}{2}$ to both sides of the inequality.

$11 x \geq \frac{5}{2}$

Divide each term in $11 x \geq \frac{5}{2}$ by $11$ and simplify.

Divide each term in $11 x \geq \frac{5}{2}$ by $11$ .

$\frac{11 x}{11} \geq \frac{\frac{5}{2}}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} \geq \frac{\frac{5}{2}}{11}$

Divide $x$ by $1$ .

$x \geq \frac{\frac{5}{2}}{11}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x \geq \frac{5}{2} \cdot \frac{1}{11}$

Multiply $\frac{5}{2} \cdot \frac{1}{11}$ .

Multiply $\frac{5}{2}$ by $\frac{1}{11}$ .

$x \geq \frac{5}{2 \cdot 11}$

Multiply $2$ by $11$ .

$x \geq \frac{5}{22}$

The result can be shown in multiple forms.

Inequality Form:

$x \geq \frac{5}{22}$

Interval Notation:

$[\frac{5}{22}, \infty)$

Solve the Inequality for x 3x-5/6>=(-2x)/3

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