Solve the Inequality for x -2(3x+2)>=-6x-4

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

Step 1

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

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply.

Multiply $3$ by $- 2$ .

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

Multiply $- 2$ by $2$ .

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

Step 2

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

Add $6 x$ to both sides of the inequality.

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

Combine the opposite terms in $- 6 x - 4 + 6 x$ .

Add $- 6 x$ and $6 x$ .

$0 - 4 \geq - 4$

Subtract $4$ from $0$ .

$- 4 \geq - 4$

Step 3

Since $- 4 = - 4$ , the equation will always be true.

Always true

Step 4

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$