Solve the Inequality for x -2(x+2)<x+8

$- 2 (x + 2) < x + 8$

Step 1

Simplify $- 2 (x + 2)$ .

Rewrite.

$0 + 0 - 2 (x + 2) < x + 8$

Simplify by adding zeros.

$- 2 (x + 2) < x + 8$

Apply the distributive property.

$- 2 x - 2 \cdot 2 < x + 8$

Multiply $- 2$ by $2$ .

$- 2 x - 4 < x + 8$

Step 2

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

Subtract $x$ from both sides of the inequality.

$- 2 x - 4 - x < 8$

Subtract $x$ from $- 2 x$ .

$- 3 x - 4 < 8$

Step 3

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

Add $4$ to both sides of the inequality.

$- 3 x < 8 + 4$

Add $8$ and $4$ .

$- 3 x < 12$

Step 4

Divide each term in $- 3 x < 12$ by $- 3$ and simplify.

Divide each term in $- 3 x < 12$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} > \frac{12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} > \frac{12}{- 3}$

Divide $x$ by $1$ .

$x > \frac{12}{- 3}$

Simplify the right side.

Divide $12$ by $- 3$ .

$x > - 4$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > - 4$

Interval Notation:

$(- 4, \infty)$

Solve the Inequality for x -2(x+2)<x+8

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