Solve for x x/2+(5x)/4=x/12

$\frac{x}{2} + \frac{5 x}{4} = \frac{x}{12}$

Step 1

Multiply both sides by $12$ .

$(\frac{x}{2} + \frac{5 x}{4}) \cdot 12 = \frac{x}{12} \cdot 12$

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{x}{2} + \frac{5 x}{4}) \cdot 12$ .

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

$(\frac{x}{2} \cdot \frac{2}{2} + \frac{5 x}{4}) \cdot 12 = \frac{x}{12} \cdot 12$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

$(\frac{x \cdot 2}{2 \cdot 2} + \frac{5 x}{4}) \cdot 12 = \frac{x}{12} \cdot 12$

Multiply $2$ by $2$ .

$(\frac{x \cdot 2}{4} + \frac{5 x}{4}) \cdot 12 = \frac{x}{12} \cdot 12$

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 5 x}{4} \cdot 12 = \frac{x}{12} \cdot 12$

Simplify the numerator.

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

$\frac{2 \cdot x + 5 x}{4} \cdot 12 = \frac{x}{12} \cdot 12$

Add $2 x$ and $5 x$ .

$\frac{7 x}{4} \cdot 12 = \frac{x}{12} \cdot 12$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$\frac{7 x}{4} \cdot (4 (3)) = \frac{x}{12} \cdot 12$

Cancel the common factor.

$\frac{7 x}{4} \cdot (4 \cdot 3) = \frac{x}{12} \cdot 12$

Rewrite the expression.

$7 x \cdot 3 = \frac{x}{12} \cdot 12$

Multiply $3$ by $7$ .

$21 x = \frac{x}{12} \cdot 12$

Simplify the right side.

Cancel the common factor of $12$ .

Cancel the common factor.

$21 x = \frac{x}{12} \cdot 12$

Rewrite the expression.

$21 x = x$

Step 3

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

$21 x - x = 0$

Subtract $x$ from $21 x$ .

$20 x = 0$

Divide each term in $20 x = 0$ by $20$ and simplify.

Divide each term in $20 x = 0$ by $20$ .

$\frac{20 x}{20} = \frac{0}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 x}{20} = \frac{0}{20}$

Divide $x$ by $1$ .

$x = \frac{0}{20}$

Simplify the right side.

Divide $0$ by $20$ .

$x = 0$

Solve for x x/2+(5x)/4=x/12

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