Solve the Absolute Value Inequality for x 2(3x-1)>=4x-6

$2 (3 x - 1) \geq 4 x - 6$

Step 1

Simplify $2 (3 x - 1)$ .

Rewrite.

$0 + 0 + 2 (3 x - 1) \geq 4 x - 6$

Simplify by adding zeros.

$2 (3 x - 1) \geq 4 x - 6$

Apply the distributive property.

$2 (3 x) + 2 \cdot - 1 \geq 4 x - 6$

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 \cdot - 1 \geq 4 x - 6$

Multiply $2$ by $- 1$ .

$6 x - 2 \geq 4 x - 6$

Step 2

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

Subtract $4 x$ from both sides of the inequality.

$6 x - 2 - 4 x \geq - 6$

Subtract $4 x$ from $6 x$ .

$2 x - 2 \geq - 6$

Step 3

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

Add $2$ to both sides of the inequality.

$2 x \geq - 6 + 2$

Add $- 6$ and $2$ .

$2 x \geq - 4$

Step 4

Divide each term in $2 x \geq - 4$ by $2$ and simplify.

Divide each term in $2 x \geq - 4$ by $2$ .

$\frac{2 x}{2} \geq \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{- 4}{2}$

Divide $x$ by $1$ .

$x \geq \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

$x \geq - 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 2$

Interval Notation:

$[- 2, \infty)$