Solve the Inequality for x 4x-2(x-3)>=0

$4 x - 2 (x - 3) \geq 0$

Step 1

Simplify $4 x - 2 (x - 3)$ .

Simplify each term.

Apply the distributive property.

$4 x - 2 x - 2 \cdot - 3 \geq 0$

Multiply $- 2$ by $- 3$ .

$4 x - 2 x + 6 \geq 0$

Subtract $2 x$ from $4 x$ .

$2 x + 6 \geq 0$

Step 2

Subtract $6$ from both sides of the inequality.

$2 x \geq - 6$

Step 3

Divide each term in $2 x \geq - 6$ by $2$ and simplify.

Divide each term in $2 x \geq - 6$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 6$ by $2$ .

$x \geq - 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 3$

Interval Notation:

$[- 3, \infty)$