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

$2 (3 x - 2) \geq 2$

Step 1

Divide each term in $2 (3 x - 2) \geq 2$ by $2$ and simplify.

Divide each term in $2 (3 x - 2) \geq 2$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $3 x - 2$ by $1$ .

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

Simplify the right side.

Divide $2$ by $2$ .

$3 x - 2 \geq 1$

Step 2

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

Add $2$ to both sides of the inequality.

$3 x \geq 1 + 2$

Add $1$ and $2$ .

$3 x \geq 3$

Step 3

Divide each term in $3 x \geq 3$ by $3$ and simplify.

Divide each term in $3 x \geq 3$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $3$ by $3$ .

$x \geq 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 1$

Interval Notation:

$[1, \infty)$