Solve the Inequality for x 2x+3+2(x+1)<-3(1-x)

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

Step 1

Simplify $2 x + 3 + 2 (x + 1)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $1$ .

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

Simplify by adding terms.

Add $2 x$ and $2 x$ .

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

Add $3$ and $2$ .

$4 x + 5 < - 3 (1 - x)$

Step 2

Simplify $- 3 (1 - x)$ .

Apply the distributive property.

$4 x + 5 < - 3 \cdot 1 - 3 (- x)$

Multiply.

Multiply $- 3$ by $1$ .

$4 x + 5 < - 3 - 3 (- x)$

Multiply $- 1$ by $- 3$ .

$4 x + 5 < - 3 + 3 x$

Step 3

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

Subtract $3 x$ from both sides of the inequality.

$4 x + 5 - 3 x < - 3$

Subtract $3 x$ from $4 x$ .

$x + 5 < - 3$

Step 4

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

Subtract $5$ from both sides of the inequality.

$x < - 3 - 5$

Subtract $5$ from $- 3$ .

$x < - 8$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < - 8$

Interval Notation:

$(- \infty, - 8)$