Solve the Inequality for x 2(x+6)<=2x+12

$2 (x + 6) \leq 2 x + 12$

Simplify $2 (x + 6)$ .

Rewrite.

$0 + 0 + 2 (x + 6) \leq 2 x + 12$

Simplify by adding zeros.

$2 (x + 6) \leq 2 x + 12$

Apply the distributive property.

$2 x + 2 \cdot 6 \leq 2 x + 12$

Multiply $2$ by $6$ .

$2 x + 12 \leq 2 x + 12$

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

Subtract $2 x$ from both sides of the inequality.

$2 x + 12 - 2 x \leq 12$

Combine the opposite terms in $2 x + 12 - 2 x$ .

Subtract $2 x$ from $2 x$ .

$0 + 12 \leq 12$

Add $0$ and $12$ .

$12 \leq 12$

Since $12 = 12$ , the equation will always be true.

Always true

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$