Solve for x 3(x+1)+11<-2(x+13)

$3 (x + 1) + 11 < - 2 (x + 13)$

Simplify $3 (x + 1) + 11$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot 1 + 11 < - 2 (x + 13)$

Multiply $3$ by $1$ .

$3 x + 3 + 11 < - 2 (x + 13)$

Add $3$ and $11$ .

$3 x + 14 < - 2 (x + 13)$

Simplify $- 2 (x + 13)$ .

Apply the distributive property.

$3 x + 14 < - 2 x - 2 \cdot 13$

Multiply $- 2$ by $13$ .

$3 x + 14 < - 2 x - 26$

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

Add $2 x$ to both sides of the inequality.

$3 x + 14 + 2 x < - 26$

Add $3 x$ and $2 x$ .

$5 x + 14 < - 26$

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

Subtract $14$ from both sides of the inequality.

$5 x < - 26 - 14$

Subtract $14$ from $- 26$ .

$5 x < - 40$

Divide each term in $5 x < - 40$ by $5$ and simplify.

Divide each term in $5 x < - 40$ by $5$ .

$\frac{5 x}{5} < \frac{- 40}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} < \frac{- 40}{5}$

Divide $x$ by $1$ .

$x < \frac{- 40}{5}$

Simplify the right side.

Divide $- 40$ by $5$ .

$x < - 8$

The result can be shown in multiple forms.

Inequality Form:

$x < - 8$

Interval Notation:

$(- \infty, - 8)$