Solve for x 2(x+2)+3x=2(x+1)+1

$2 (x + 2) + 3 x = 2 (x + 1) + 1$

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

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot 2 + 3 x = 2 (x + 1) + 1$

Multiply $2$ by $2$ .

$2 x + 4 + 3 x = 2 (x + 1) + 1$

Add $2 x$ and $3 x$ .

$5 x + 4 = 2 (x + 1) + 1$

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

Simplify each term.

Apply the distributive property.

$5 x + 4 = 2 x + 2 \cdot 1 + 1$

Multiply $2$ by $1$ .

$5 x + 4 = 2 x + 2 + 1$

Add $2$ and $1$ .

$5 x + 4 = 2 x + 3$

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

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

$5 x + 4 - 2 x = 3$

Subtract $2 x$ from $5 x$ .

$3 x + 4 = 3$

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

Subtract $4$ from both sides of the equation.

$3 x = 3 - 4$

Subtract $4$ from $3$ .

$3 x = - 1$

Divide each term in $3 x = - 1$ by $3$ and simplify.

Divide each term in $3 x = - 1$ by $3$ .

$\frac{3 x}{3} = \frac{- 1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 1}{3}$

Divide $x$ by $1$ .

$x = \frac{- 1}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{3}$

Decimal Form:

$x = - 0.\overline{3}$