Solve for x 5+(3x+1)=5(x+1)+2

$5 + (3 x + 1) = 5 (x + 1) + 2$

Step 1

Add $5$ and $1$ .

$3 x + 6 = 5 (x + 1) + 2$

Step 2

Simplify $5 (x + 1) + 2$ .

Simplify each term.

Apply the distributive property.

$3 x + 6 = 5 x + 5 \cdot 1 + 2$

Multiply $5$ by $1$ .

$3 x + 6 = 5 x + 5 + 2$

Add $5$ and $2$ .

$3 x + 6 = 5 x + 7$

Step 3

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

Subtract $5 x$ from both sides of the equation.

$3 x + 6 - 5 x = 7$

Subtract $5 x$ from $3 x$ .

$- 2 x + 6 = 7$

Step 4

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

Subtract $6$ from both sides of the equation.

$- 2 x = 7 - 6$

Subtract $6$ from $7$ .

$- 2 x = 1$

Step 5

Divide each term in $- 2 x = 1$ by $- 2$ and simplify.

Divide each term in $- 2 x = 1$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{1}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{1}{- 2}$

Divide $x$ by $1$ .

$x = \frac{1}{- 2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}$

Decimal Form:

$x = - 0.5$