Solve for x 9x-2-7x(1/x-1/2)=(1+x/2)/2+11/4

$9 x - 2 - 7 x (\frac{1}{x} - \frac{1}{2}) = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Simplify $9 x - 2 - 7 x (\frac{1}{x} - \frac{1}{2})$ .

Simplify each term.

Apply the distributive property.

$9 x - 2 - 7 x \frac{1}{x} - 7 x (- \frac{1}{2}) = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Cancel the common factor of $x$ .

Factor $x$ out of $- 7 x$ .

$9 x - 2 + x \cdot - 7 \frac{1}{x} - 7 x (- \frac{1}{2}) = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Cancel the common factor.

$9 x - 2 + x \cdot - 7 \frac{1}{x} - 7 x (- \frac{1}{2}) = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Rewrite the expression.

$9 x - 2 - 7 - 7 x (- \frac{1}{2}) = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Multiply $- 7 x (- \frac{1}{2})$ .

Multiply $- 1$ by $- 7$ .

$9 x - 2 - 7 + 7 x \frac{1}{2} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Combine $7$ and $\frac{1}{2}$ .

$9 x - 2 - 7 + x \frac{7}{2} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Combine $x$ and $\frac{7}{2}$ .

$9 x - 2 - 7 + \frac{x \cdot 7}{2} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

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

$9 x - 2 - 7 + \frac{7 x}{2} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

To write $9 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$9 x \cdot \frac{2}{2} + \frac{7 x}{2} - 2 - 7 = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Combine $9 x$ and $\frac{2}{2}$ .

$\frac{9 x \cdot 2}{2} + \frac{7 x}{2} - 2 - 7 = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Combine the numerators over the common denominator.

$\frac{9 x \cdot 2 + 7 x}{2} - 2 - 7 = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Find the common denominator.

Write $- 2$ as a fraction with denominator $1$ .

$\frac{9 x \cdot 2 + 7 x}{2} + \frac{- 2}{1} - 7 = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Multiply $\frac{- 2}{1}$ by $\frac{2}{2}$ .

$\frac{9 x \cdot 2 + 7 x}{2} + \frac{- 2}{1} \cdot \frac{2}{2} - 7 = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Multiply $\frac{- 2}{1}$ by $\frac{2}{2}$ .

$\frac{9 x \cdot 2 + 7 x}{2} + \frac{- 2 \cdot 2}{2} - 7 = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Write $- 7$ as a fraction with denominator $1$ .

$\frac{9 x \cdot 2 + 7 x}{2} + \frac{- 2 \cdot 2}{2} + \frac{- 7}{1} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Multiply $\frac{- 7}{1}$ by $\frac{2}{2}$ .

$\frac{9 x \cdot 2 + 7 x}{2} + \frac{- 2 \cdot 2}{2} + \frac{- 7}{1} \cdot \frac{2}{2} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Multiply $\frac{- 7}{1}$ by $\frac{2}{2}$ .

$\frac{9 x \cdot 2 + 7 x}{2} + \frac{- 2 \cdot 2}{2} + \frac{- 7 \cdot 2}{2} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Combine the numerators over the common denominator.

$\frac{9 x \cdot 2 + 7 x - 2 \cdot 2 - 7 \cdot 2}{2} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Simplify each term.

Multiply $2$ by $9$ .

$\frac{18 x + 7 x - 2 \cdot 2 - 7 \cdot 2}{2} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Multiply $- 2$ by $2$ .

$\frac{18 x + 7 x - 4 - 7 \cdot 2}{2} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Multiply $- 7$ by $2$ .

$\frac{18 x + 7 x - 4 - 14}{2} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Simplify by adding terms.

Add $18 x$ and $7 x$ .

$\frac{25 x - 4 - 14}{2} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Subtract $14$ from $- 4$ .

$\frac{25 x - 18}{2} = \frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$

Simplify $\frac{1 + \frac{x}{2}}{2} + \frac{11}{4}$ .

Simplify each term.

Simplify the numerator.

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

$\frac{25 x - 18}{2} = \frac{\frac{2}{2} + \frac{x}{2}}{2} + \frac{11}{4}$

Combine the numerators over the common denominator.

$\frac{25 x - 18}{2} = \frac{\frac{2 + x}{2}}{2} + \frac{11}{4}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{25 x - 18}{2} = \frac{2 + x}{2} \cdot \frac{1}{2} + \frac{11}{4}$

Multiply $\frac{2 + x}{2} \cdot \frac{1}{2}$ .

Multiply $\frac{2 + x}{2}$ by $\frac{1}{2}$ .

$\frac{25 x - 18}{2} = \frac{2 + x}{2 \cdot 2} + \frac{11}{4}$

Multiply $2$ by $2$ .

$\frac{25 x - 18}{2} = \frac{2 + x}{4} + \frac{11}{4}$

Combine fractions.

Combine the numerators over the common denominator.

$\frac{25 x - 18}{2} = \frac{2 + x + 11}{4}$

Add $2$ and $11$ .

$\frac{25 x - 18}{2} = \frac{x + 13}{4}$

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

Subtract $\frac{x + 13}{4}$ from both sides of the equation.

$\frac{25 x - 18}{2} - \frac{x + 13}{4} = 0$

To write $\frac{25 x - 18}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{25 x - 18}{2} \cdot \frac{2}{2} - \frac{x + 13}{4} = 0$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{25 x - 18}{2}$ by $\frac{2}{2}$ .

$\frac{(25 x - 18) \cdot 2}{2 \cdot 2} - \frac{x + 13}{4} = 0$

Multiply $2$ by $2$ .

$\frac{(25 x - 18) \cdot 2}{4} - \frac{x + 13}{4} = 0$

Combine the numerators over the common denominator.

$\frac{(25 x - 18) \cdot 2 - (x + 13)}{4} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{25 x \cdot 2 - 18 \cdot 2 - (x + 13)}{4} = 0$

Multiply $2$ by $25$ .

$\frac{50 x - 18 \cdot 2 - (x + 13)}{4} = 0$

Multiply $- 18$ by $2$ .

$\frac{50 x - 36 - (x + 13)}{4} = 0$

Apply the distributive property.

$\frac{50 x - 36 - x - 1 \cdot 13}{4} = 0$

Multiply $- 1$ by $13$ .

$\frac{50 x - 36 - x - 13}{4} = 0$

Subtract $x$ from $50 x$ .

$\frac{49 x - 36 - 13}{4} = 0$

Subtract $13$ from $- 36$ .

$\frac{49 x - 49}{4} = 0$

Factor $49$ out of $49 x - 49$ .

Factor $49$ out of $49 x$ .

$\frac{49 (x) - 49}{4} = 0$

Factor $49$ out of $- 49$ .

$\frac{49 (x) + 49 (- 1)}{4} = 0$

Factor $49$ out of $49 (x) + 49 (- 1)$ .

$\frac{49 (x - 1)}{4} = 0$

Set the numerator equal to zero.

$49 (x - 1) = 0$

Solve the equation for $x$ .

Divide each term in $49 (x - 1) = 0$ by $49$ and simplify.

Divide each term in $49 (x - 1) = 0$ by $49$ .

$\frac{49 (x - 1)}{49} = \frac{0}{49}$

Simplify the left side.

Cancel the common factor of $49$ .

Cancel the common factor.

$\frac{49 (x - 1)}{49} = \frac{0}{49}$

Divide $x - 1$ by $1$ .

$x - 1 = \frac{0}{49}$

Simplify the right side.

Divide $0$ by $49$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Solve for x 9x-2-7x(1/x-1/2)=(1+x/2)/2+11/4

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