Solve for x 4-(x+2)<-3(x+4)

$4 - (x + 2) < - 3 (x + 4)$

Step 1

Simplify $4 - (x + 2)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- 1$ by $2$ .

$4 - x - 2 < - 3 (x + 4)$

Subtract $2$ from $4$ .

$- x + 2 < - 3 (x + 4)$

Step 2

Simplify $- 3 (x + 4)$ .

Apply the distributive property.

$- x + 2 < - 3 x - 3 \cdot 4$

Multiply $- 3$ by $4$ .

$- x + 2 < - 3 x - 12$

Step 3

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

Add $3 x$ to both sides of the inequality.

$- x + 2 + 3 x < - 12$

Add $- x$ and $3 x$ .

$2 x + 2 < - 12$

Step 4

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

Subtract $2$ from both sides of the inequality.

$2 x < - 12 - 2$

Subtract $2$ from $- 12$ .

$2 x < - 14$

Step 5

Divide each term in $2 x < - 14$ by $2$ and simplify.

Divide each term in $2 x < - 14$ by $2$ .

$\frac{2 x}{2} < \frac{- 14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{- 14}{2}$

Divide $x$ by $1$ .

$x < \frac{- 14}{2}$

Simplify the right side.

Divide $- 14$ by $2$ .

$x < - 7$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < - 7$

Interval Notation:

$(- \infty, - 7)$

Solve for x 4-(x+2)<-3(x+4)

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