Solve for x x+x/7+1/11(x+x/7)=60

$x + \frac{x}{7} + \frac{1}{11} (x + \frac{x}{7}) = 60$

Simplify $x + \frac{x}{7} + \frac{1}{11} \cdot (x + \frac{x}{7})$ .

Simplify each term.

To write $x$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x + \frac{x}{7} + \frac{1}{11} \cdot (x \cdot \frac{7}{7} + \frac{x}{7}) = 60$

Combine $x$ and $\frac{7}{7}$ .

$x + \frac{x}{7} + \frac{1}{11} \cdot (\frac{x \cdot 7}{7} + \frac{x}{7}) = 60$

Combine the numerators over the common denominator.

$x + \frac{x}{7} + \frac{1}{11} \cdot \frac{x \cdot 7 + x}{7} = 60$

Simplify the numerator.

Move $7$ to the left of $x$ .

$x + \frac{x}{7} + \frac{1}{11} \cdot \frac{7 \cdot x + x}{7} = 60$

Add $7 x$ and $x$ .

$x + \frac{x}{7} + \frac{1}{11} \cdot \frac{8 x}{7} = 60$

Multiply $\frac{1}{11} \cdot \frac{8 x}{7}$ .

Multiply $\frac{1}{11}$ by $\frac{8 x}{7}$ .

$x + \frac{x}{7} + \frac{8 x}{11 \cdot 7} = 60$

Multiply $11$ by $7$ .

$x + \frac{x}{7} + \frac{8 x}{77} = 60$

Find the common denominator.

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

$\frac{x}{1} + \frac{x}{7} + \frac{8 x}{77} = 60$

Multiply $\frac{x}{1}$ by $\frac{77}{77}$ .

$\frac{x}{1} \cdot \frac{77}{77} + \frac{x}{7} + \frac{8 x}{77} = 60$

Multiply $\frac{x}{1}$ by $\frac{77}{77}$ .

$\frac{x \cdot 77}{77} + \frac{x}{7} + \frac{8 x}{77} = 60$

Multiply $\frac{x}{7}$ by $\frac{11}{11}$ .

$\frac{x \cdot 77}{77} + \frac{x}{7} \cdot \frac{11}{11} + \frac{8 x}{77} = 60$

Multiply $\frac{x}{7}$ by $\frac{11}{11}$ .

$\frac{x \cdot 77}{77} + \frac{x \cdot 11}{7 \cdot 11} + \frac{8 x}{77} = 60$

Multiply $7$ by $11$ .

$\frac{x \cdot 77}{77} + \frac{x \cdot 11}{77} + \frac{8 x}{77} = 60$

Combine the numerators over the common denominator.

$\frac{x \cdot 77 + x \cdot 11 + 8 x}{77} = 60$

Simplify each term.

Move $77$ to the left of $x$ .

$\frac{77 \cdot x + x \cdot 11 + 8 x}{77} = 60$

Move $11$ to the left of $x$ .

$\frac{77 x + 11 x + 8 x}{77} = 60$

Simplify by adding terms.

Add $77 x$ and $11 x$ .

$\frac{88 x + 8 x}{77} = 60$

Add $88 x$ and $8 x$ .

$\frac{96 x}{77} = 60$

Multiply both sides of the equation by $\frac{77}{96}$ .

$\frac{77}{96} \cdot \frac{96 x}{77} = \frac{77}{96} \cdot 60$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{77}{96} \cdot \frac{96 x}{77}$ .

Cancel the common factor of $77$ .

Cancel the common factor.

$\frac{77}{96} \cdot \frac{96 x}{77} = \frac{77}{96} \cdot 60$

Rewrite the expression.

$\frac{1}{96} (96 x) = \frac{77}{96} \cdot 60$

Cancel the common factor of $96$ .

Factor $96$ out of $96 x$ .

$\frac{1}{96} (96 (x)) = \frac{77}{96} \cdot 60$

Cancel the common factor.

$\frac{1}{96} (96 x) = \frac{77}{96} \cdot 60$

Rewrite the expression.

$x = \frac{77}{96} \cdot 60$

Simplify the right side.

Simplify $\frac{77}{96} \cdot 60$ .

Cancel the common factor of $12$ .

Factor $12$ out of $96$ .

$x = \frac{77}{12 (8)} \cdot 60$

Factor $12$ out of $60$ .

$x = \frac{77}{12 \cdot 8} \cdot (12 \cdot 5)$

Cancel the common factor.

$x = \frac{77}{12 \cdot 8} \cdot (12 \cdot 5)$

Rewrite the expression.

$x = \frac{77}{8} \cdot 5$

Combine $\frac{77}{8}$ and $5$ .

$x = \frac{77 \cdot 5}{8}$

Multiply $77$ by $5$ .

$x = \frac{385}{8}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{385}{8}$

Decimal Form:

$x = 48.125$

Mixed Number Form:

$x = 48 \frac{1}{8}$

Solve for x x+x/7+1/11(x+x/7)=60

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