Solve for x (3(x+4))/2+1=-7

$\frac{3 (x + 4)}{2} + 1 = - 7$

Simplify $\frac{3 (x + 4)}{2} + 1$ .

Combine into one fraction.

Write $1$ as a fraction with a common denominator.

$\frac{3 (x + 4)}{2} + \frac{2}{2} = - 7$

Combine the numerators over the common denominator.

$\frac{3 (x + 4) + 2}{2} = - 7$

Simplify the numerator.

Apply the distributive property.

$\frac{3 x + 3 \cdot 4 + 2}{2} = - 7$

Multiply $3$ by $4$ .

$\frac{3 x + 12 + 2}{2} = - 7$

Add $12$ and $2$ .

$\frac{3 x + 14}{2} = - 7$

Multiply both sides by $2$ .

$\frac{3 x + 14}{2} \cdot 2 = - 7 \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 x + 14}{2} \cdot 2 = - 7 \cdot 2$

Rewrite the expression.

$3 x + 14 = - 7 \cdot 2$

Simplify the right side.

Multiply $- 7$ by $2$ .

$3 x + 14 = - 14$

Solve for $x$ .

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

Subtract $14$ from both sides of the equation.

$3 x = - 14 - 14$

Subtract $14$ from $- 14$ .

$3 x = - 28$

Divide each term in $3 x = - 28$ by $3$ and simplify.

Divide each term in $3 x = - 28$ by $3$ .

$\frac{3 x}{3} = \frac{- 28}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 28}{3}$

Divide $x$ by $1$ .

$x = \frac{- 28}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{28}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{28}{3}$

Decimal Form:

$x = - 9.\overline{3}$

Mixed Number Form:

$x = - 9 \frac{1}{3}$

Solve for x (3(x+4))/2+1=-7

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