Solve the Inequality for x 1/6x>=-5/6x+2/3

$\frac{1}{6} x \geq - \frac{5}{6} x + \frac{2}{3}$

Step 1

Simplify $\frac{1}{6} x$ .

Rewrite.

$0 + 0 + \frac{1}{6} x \geq - \frac{5}{6} x + \frac{2}{3}$

Simplify by adding zeros.

$\frac{1}{6} x \geq - \frac{5}{6} x + \frac{2}{3}$

Combine $\frac{1}{6}$ and $x$ .

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

Step 2

Simplify each term.

Combine $x$ and $\frac{5}{6}$ .

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

Move $5$ to the left of $x$ .

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

Step 3

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

Add $\frac{5 x}{6}$ to both sides of the inequality.

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

Combine the numerators over the common denominator.

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

Add $x$ and $5 x$ .

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

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 4

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$[\frac{2}{3}, \infty)$