Solve for x 2x+3/4*(4x+16)=7

$2 x + \frac{3}{4} \cdot (4 x + 16) = 7$

Step 1

Simplify $2 x + \frac{3}{4} \cdot (4 x + 16)$ .

Simplify each term.

Apply the distributive property.

$2 x + \frac{3}{4} (4 x) + \frac{3}{4} \cdot 16 = 7$

Cancel the common factor of $4$ .

Factor $4$ out of $4 x$ .

$2 x + \frac{3}{4} (4 (x)) + \frac{3}{4} \cdot 16 = 7$

Cancel the common factor.

$2 x + \frac{3}{4} (4 x) + \frac{3}{4} \cdot 16 = 7$

Rewrite the expression.

$2 x + 3 x + \frac{3}{4} \cdot 16 = 7$

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2 x + 3 x + 3 \cdot 4 = 7$

Multiply $3$ by $4$ .

$2 x + 3 x + 12 = 7$

Add $2 x$ and $3 x$ .

$5 x + 12 = 7$

Step 2

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

Subtract $12$ from both sides of the equation.

$5 x = 7 - 12$

Subtract $12$ from $7$ .

$5 x = - 5$

Step 3

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

Divide each term in $5 x = - 5$ by $5$ .

$\frac{5 x}{5} = \frac{- 5}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 5}{5}$

Divide $x$ by $1$ .

$x = \frac{- 5}{5}$

Simplify the right side.

Divide $- 5$ by $5$ .

$x = - 1$