Solve for x x/5=x/6+1

$\frac{x}{5} = \frac{x}{6} + 1$

Step 1

Multiply both sides by $5$ .

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

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

Simplify terms.

Apply the distributive property.

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

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

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

Multiply $5$ by $1$ .

$x = \frac{x \cdot 5}{6} + 5$

Move $5$ to the left of $x$ .

$x = \frac{5 x}{6} + 5$

Step 3

Solve for $x$ .

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

Subtract $\frac{5 x}{6}$ from both sides of the equation.

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

To write $x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

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

Subtract $5 x$ from $6 x$ .

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

Multiply both sides of the equation by $6$ .

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

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

$x = 6 \cdot 5$

Simplify the right side.

Multiply $6$ by $5$ .

$x = 30$

Solve for x x/5=x/6+1

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