Solve for x x+x+1/6x=13

$x + x + \frac{1}{6} x = 13$

Step 1

Simplify $x + x + \frac{1}{6} x$ .

Combine $\frac{1}{6}$ and $x$ .

$x + x + \frac{x}{6} = 13$

Find the common denominator.

Write $x$ as a fraction with denominator $1$ .

$\frac{x}{1} + x + \frac{x}{6} = 13$

Multiply $\frac{x}{1}$ by $\frac{6}{6}$ .

$\frac{x}{1} \cdot \frac{6}{6} + x + \frac{x}{6} = 13$

Multiply $\frac{x}{1}$ by $\frac{6}{6}$ .

$\frac{x \cdot 6}{6} + x + \frac{x}{6} = 13$

Write $x$ as a fraction with denominator $1$ .

$\frac{x \cdot 6}{6} + \frac{x}{1} + \frac{x}{6} = 13$

Multiply $\frac{x}{1}$ by $\frac{6}{6}$ .

$\frac{x \cdot 6}{6} + \frac{x}{1} \cdot \frac{6}{6} + \frac{x}{6} = 13$

Multiply $\frac{x}{1}$ by $\frac{6}{6}$ .

$\frac{x \cdot 6}{6} + \frac{x \cdot 6}{6} + \frac{x}{6} = 13$

Combine the numerators over the common denominator.

$\frac{x \cdot 6 + x \cdot 6 + x}{6} = 13$

Simplify each term.

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

$\frac{6 \cdot x + x \cdot 6 + x}{6} = 13$

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

$\frac{6 x + 6 x + x}{6} = 13$

Simplify by adding terms.

Add $6 x$ and $6 x$ .

$\frac{12 x + x}{6} = 13$

Add $12 x$ and $x$ .

$\frac{13 x}{6} = 13$

Step 2

Multiply both sides of the equation by $\frac{6}{13}$ .

$\frac{6}{13} \cdot \frac{13 x}{6} = \frac{6}{13} \cdot 13$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{13} \cdot \frac{13 x}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{13} \cdot \frac{13 x}{6} = \frac{6}{13} \cdot 13$

Rewrite the expression.

$\frac{1}{13} (13 x) = \frac{6}{13} \cdot 13$

Cancel the common factor of $13$ .

Factor $13$ out of $13 x$ .

$\frac{1}{13} (13 (x)) = \frac{6}{13} \cdot 13$

Cancel the common factor.

$\frac{1}{13} (13 x) = \frac{6}{13} \cdot 13$

Rewrite the expression.

$x = \frac{6}{13} \cdot 13$

Simplify the right side.

Cancel the common factor of $13$ .

Cancel the common factor.

$x = \frac{6}{13} \cdot 13$

Rewrite the expression.

$x = 6$

Solve for x x+x+1/6x=13

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