Solve for x (9x+7)/2-x+(x-2)/7=36

$\frac{9 x + 7}{2} - x + \frac{x - 2}{7} = 36$

Simplify $\frac{9 x + 7}{2} - x + \frac{x - 2}{7}$ .

Find the common denominator.

Multiply $\frac{9 x + 7}{2}$ by $\frac{7}{7}$ .

$\frac{9 x + 7}{2} \cdot \frac{7}{7} - x + \frac{x - 2}{7} = 36$

Multiply $\frac{9 x + 7}{2}$ by $\frac{7}{7}$ .

$\frac{(9 x + 7) \cdot 7}{2 \cdot 7} - x + \frac{x - 2}{7} = 36$

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

$\frac{(9 x + 7) \cdot 7}{2 \cdot 7} + \frac{- x}{1} + \frac{x - 2}{7} = 36$

Multiply $\frac{- x}{1}$ by $\frac{14}{14}$ .

$\frac{(9 x + 7) \cdot 7}{2 \cdot 7} + \frac{- x}{1} \cdot \frac{14}{14} + \frac{x - 2}{7} = 36$

Multiply $\frac{- x}{1}$ by $\frac{14}{14}$ .

$\frac{(9 x + 7) \cdot 7}{2 \cdot 7} + \frac{- x \cdot 14}{14} + \frac{x - 2}{7} = 36$

Multiply $\frac{x - 2}{7}$ by $\frac{2}{2}$ .

$\frac{(9 x + 7) \cdot 7}{2 \cdot 7} + \frac{- x \cdot 14}{14} + \frac{x - 2}{7} \cdot \frac{2}{2} = 36$

Multiply $\frac{x - 2}{7}$ by $\frac{2}{2}$ .

$\frac{(9 x + 7) \cdot 7}{2 \cdot 7} + \frac{- x \cdot 14}{14} + \frac{(x - 2) \cdot 2}{7 \cdot 2} = 36$

Multiply $2$ by $7$ .

$\frac{(9 x + 7) \cdot 7}{14} + \frac{- x \cdot 14}{14} + \frac{(x - 2) \cdot 2}{7 \cdot 2} = 36$

Reorder the factors of $7 \cdot 2$ .

$\frac{(9 x + 7) \cdot 7}{14} + \frac{- x \cdot 14}{14} + \frac{(x - 2) \cdot 2}{2 \cdot 7} = 36$

Multiply $2$ by $7$ .

$\frac{(9 x + 7) \cdot 7}{14} + \frac{- x \cdot 14}{14} + \frac{(x - 2) \cdot 2}{14} = 36$

Combine the numerators over the common denominator.

$\frac{(9 x + 7) \cdot 7 - x \cdot 14 + (x - 2) \cdot 2}{14} = 36$

Simplify each term.

Apply the distributive property.

$\frac{9 x \cdot 7 + 7 \cdot 7 - x \cdot 14 + (x - 2) \cdot 2}{14} = 36$

Multiply $7$ by $9$ .

$\frac{63 x + 7 \cdot 7 - x \cdot 14 + (x - 2) \cdot 2}{14} = 36$

Multiply $7$ by $7$ .

$\frac{63 x + 49 - x \cdot 14 + (x - 2) \cdot 2}{14} = 36$

Multiply $14$ by $- 1$ .

$\frac{63 x + 49 - 14 x + (x - 2) \cdot 2}{14} = 36$

Apply the distributive property.

$\frac{63 x + 49 - 14 x + x \cdot 2 - 2 \cdot 2}{14} = 36$

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

$\frac{63 x + 49 - 14 x + 2 \cdot x - 2 \cdot 2}{14} = 36$

Multiply $- 2$ by $2$ .

$\frac{63 x + 49 - 14 x + 2 x - 4}{14} = 36$

Simplify terms.

Subtract $14 x$ from $63 x$ .

$\frac{49 x + 49 + 2 x - 4}{14} = 36$

Add $49 x$ and $2 x$ .

$\frac{51 x + 49 - 4}{14} = 36$

Subtract $4$ from $49$ .

$\frac{51 x + 45}{14} = 36$

Factor $3$ out of $51 x + 45$ .

Factor $3$ out of $51 x$ .

$\frac{3 (17 x) + 45}{14} = 36$

Factor $3$ out of $45$ .

$\frac{3 (17 x) + 3 (15)}{14} = 36$

Factor $3$ out of $3 (17 x) + 3 (15)$ .

$\frac{3 (17 x + 15)}{14} = 36$

Multiply both sides by $14$ .

$\frac{3 (17 x + 15)}{14} \cdot 14 = 36 \cdot 14$

Simplify.

Simplify the left side.

Simplify $\frac{3 (17 x + 15)}{14} \cdot 14$ .

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{3 (17 x + 15)}{14} \cdot 14 = 36 \cdot 14$

Rewrite the expression.

$3 (17 x + 15) = 36 \cdot 14$

Apply the distributive property.

$3 (17 x) + 3 \cdot 15 = 36 \cdot 14$

Multiply.

Multiply $17$ by $3$ .

$51 x + 3 \cdot 15 = 36 \cdot 14$

Multiply $3$ by $15$ .

$51 x + 45 = 36 \cdot 14$

Simplify the right side.

Multiply $36$ by $14$ .

$51 x + 45 = 504$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $45$ from both sides of the equation.

$51 x = 504 - 45$

Subtract $45$ from $504$ .

$51 x = 459$

Divide each term in $51 x = 459$ by $51$ and simplify.

Divide each term in $51 x = 459$ by $51$ .

$\frac{51 x}{51} = \frac{459}{51}$

Simplify the left side.

Cancel the common factor of $51$ .

Cancel the common factor.

$\frac{51 x}{51} = \frac{459}{51}$

Divide $x$ by $1$ .

$x = \frac{459}{51}$

Simplify the right side.

Divide $459$ by $51$ .

$x = 9$

Solve for x (9x+7)/2-x+(x-2)/7=36

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