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

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

Step 1

Simplify $\frac{x + 2}{3} + \frac{2 x - 4}{4}$ .

Cancel the common factor of $2 x - 4$ and $4$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 4$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

To write $\frac{x + 2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

To write $\frac{x - 2}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 2}{3}$ by $\frac{2}{2}$ .

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

Multiply $3$ by $2$ .

$\frac{(x + 2) \cdot 2}{6} + \frac{x - 2}{2} \cdot \frac{3}{3} = 3$

Multiply $\frac{x - 2}{2}$ by $\frac{3}{3}$ .

$\frac{(x + 2) \cdot 2}{6} + \frac{(x - 2) \cdot 3}{2 \cdot 3} = 3$

Multiply $2$ by $3$ .

$\frac{(x + 2) \cdot 2}{6} + \frac{(x - 2) \cdot 3}{6} = 3$

Combine the numerators over the common denominator.

$\frac{(x + 2) \cdot 2 + (x - 2) \cdot 3}{6} = 3$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 2 + 2 \cdot 2 + (x - 2) \cdot 3}{6} = 3$

Move $2$ to the left of $x$ .

$\frac{2 \cdot x + 2 \cdot 2 + (x - 2) \cdot 3}{6} = 3$

Multiply $2$ by $2$ .

$\frac{2 \cdot x + 4 + (x - 2) \cdot 3}{6} = 3$

Apply the distributive property.

$\frac{2 x + 4 + x \cdot 3 - 2 \cdot 3}{6} = 3$

Move $3$ to the left of $x$ .

$\frac{2 x + 4 + 3 \cdot x - 2 \cdot 3}{6} = 3$

Multiply $- 2$ by $3$ .

$\frac{2 x + 4 + 3 \cdot x - 6}{6} = 3$

Add $2 x$ and $3 x$ .

$\frac{5 x + 4 - 6}{6} = 3$

Subtract $6$ from $4$ .

$\frac{5 x - 2}{6} = 3$

Step 2

Multiply both sides by $6$ .

$\frac{5 x - 2}{6} \cdot 6 = 3 \cdot 6$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{5 x - 2}{6} \cdot 6 = 3 \cdot 6$

Rewrite the expression.

$5 x - 2 = 3 \cdot 6$

Simplify the right side.

Multiply $3$ by $6$ .

$5 x - 2 = 18$

Step 4

Solve for $x$ .

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

Add $2$ to both sides of the equation.

$5 x = 18 + 2$

Add $18$ and $2$ .

$5 x = 20$

Divide each term in $5 x = 20$ by $5$ and simplify.

Divide each term in $5 x = 20$ by $5$ .

$\frac{5 x}{5} = \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{20}{5}$

Divide $x$ by $1$ .

$x = \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$x = 4$

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

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