Solve for x 3/4(2x+4)=x+19

$\frac{3}{4} (2 x + 4) = x + 19$

Step 1

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

Rewrite.

$0 + 0 + \frac{3}{4} \cdot (2 x + 4) = x + 19$

Simplify by adding zeros.

$\frac{3}{4} \cdot (2 x + 4) = x + 19$

Apply the distributive property.

$\frac{3}{4} (2 x) + \frac{3}{4} \cdot 4 = x + 19$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3}{2 (2)} (2 x) + \frac{3}{4} \cdot 4 = x + 19$

Factor $2$ out of $2 x$ .

$\frac{3}{2 (2)} (2 (x)) + \frac{3}{4} \cdot 4 = x + 19$

Cancel the common factor.

$\frac{3}{2 \cdot 2} (2 x) + \frac{3}{4} \cdot 4 = x + 19$

Rewrite the expression.

$\frac{3}{2} x + \frac{3}{4} \cdot 4 = x + 19$

Combine $\frac{3}{2}$ and $x$ .

$\frac{3 x}{2} + \frac{3}{4} \cdot 4 = x + 19$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 x}{2} + \frac{3}{4} \cdot 4 = x + 19$

Rewrite the expression.

$\frac{3 x}{2} + 3 = x + 19$

Step 2

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

Subtract $x$ from both sides of the equation.

$\frac{3 x}{2} + 3 - x = 19$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{2} - x \cdot \frac{2}{2} + 3 = 19$

Combine $- x$ and $\frac{2}{2}$ .

$\frac{3 x}{2} + \frac{- x \cdot 2}{2} + 3 = 19$

Combine the numerators over the common denominator.

$\frac{3 x - x \cdot 2}{2} + 3 = 19$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $3 x - x \cdot 2$ .

Factor $x$ out of $3 x$ .

$\frac{x \cdot 3 - x \cdot 2}{2} + 3 = 19$

Factor $x$ out of $- x \cdot 2$ .

$\frac{x \cdot 3 + x (- 1 \cdot 2)}{2} + 3 = 19$

Factor $x$ out of $x \cdot 3 + x (- 1 \cdot 2)$ .

$\frac{x (3 - 1 \cdot 2)}{2} + 3 = 19$

Multiply $- 1$ by $2$ .

$\frac{x (3 - 2)}{2} + 3 = 19$

Subtract $2$ from $3$ .

$\frac{x \cdot 1}{2} + 3 = 19$

Multiply $x$ by $1$ .

$\frac{x}{2} + 3 = 19$

Step 3

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

Subtract $3$ from both sides of the equation.

$\frac{x}{2} = 19 - 3$

Subtract $3$ from $19$ .

$\frac{x}{2} = 16$

Step 4

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 16$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 16$

Rewrite the expression.

$x = 2 \cdot 16$

Simplify the right side.

Multiply $2$ by $16$ .

$x = 32$

Solve for x 3/4(2x+4)=x+19

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