Solve for x x/5-1/2=x/6

$\frac{x}{5} - \frac{1}{2} = \frac{x}{6}$

Step 1

Multiply both sides by $6$ .

$(\frac{x}{5} - \frac{1}{2}) \cdot 6 = \frac{x}{6} \cdot 6$

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{x}{5} - \frac{1}{2}) \cdot 6$ .

Simplify terms.

Apply the distributive property.

$\frac{x}{5} \cdot 6 - \frac{1}{2} \cdot 6 = \frac{x}{6} \cdot 6$

Combine $\frac{x}{5}$ and $6$ .

$\frac{x \cdot 6}{5} - \frac{1}{2} \cdot 6 = \frac{x}{6} \cdot 6$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{x \cdot 6}{5} + \frac{- 1}{2} \cdot 6 = \frac{x}{6} \cdot 6$

Factor $2$ out of $6$ .

$\frac{x \cdot 6}{5} + \frac{- 1}{2} \cdot (2 (3)) = \frac{x}{6} \cdot 6$

Cancel the common factor.

$\frac{x \cdot 6}{5} + \frac{- 1}{2} \cdot (2 \cdot 3) = \frac{x}{6} \cdot 6$

Rewrite the expression.

$\frac{x \cdot 6}{5} - 1 \cdot 3 = \frac{x}{6} \cdot 6$

Multiply $- 1$ by $3$ .

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

Move $6$ to the left of $x$ .

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

Simplify the right side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

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

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.

$\frac{6 x}{5} - 3 - x = 0$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6 x}{5} - x \cdot \frac{5}{5} - 3 = 0$

Combine $- x$ and $\frac{5}{5}$ .

$\frac{6 x}{5} + \frac{- x \cdot 5}{5} - 3 = 0$

Combine the numerators over the common denominator.

$\frac{6 x - x \cdot 5}{5} - 3 = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $6 x - x \cdot 5$ .

Factor $x$ out of $6 x$ .

$\frac{x \cdot 6 - x \cdot 5}{5} - 3 = 0$

Factor $x$ out of $- x \cdot 5$ .

$\frac{x \cdot 6 + x (- 1 \cdot 5)}{5} - 3 = 0$

Factor $x$ out of $x \cdot 6 + x (- 1 \cdot 5)$ .

$\frac{x (6 - 1 \cdot 5)}{5} - 3 = 0$

Multiply $- 1$ by $5$ .

$\frac{x (6 - 5)}{5} - 3 = 0$

Subtract $5$ from $6$ .

$\frac{x \cdot 1}{5} - 3 = 0$

Multiply $x$ by $1$ .

$\frac{x}{5} - 3 = 0$

Add $3$ to both sides of the equation.

$\frac{x}{5} = 3$

Multiply both sides of the equation by $5$ .

$5 \frac{x}{5} = 5 \cdot 3$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{x}{5} = 5 \cdot 3$

Rewrite the expression.

$x = 5 \cdot 3$

Simplify the right side.

Multiply $5$ by $3$ .

$x = 15$

Solve for x x/5-1/2=x/6

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