Solve 7-9/11-frac{9{x-2}}=4

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

Solve for x

$$x = \frac{25}{8} = 3\frac{1}{8} = 3.125$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 11 times \frac{x-2}{x-2}.

$$7-\frac{9}{\frac{11\left(x-2\right)}{x-2}-\frac{9}{x-2}}=4$$

Since \frac{11\left(x-2\right)}{x-2} and \frac{9}{x-2} have the same denominator, subtract them by subtracting their numerators.

$$7-\frac{9}{\frac{11\left(x-2\right)-9}{x-2}}=4$$

Do the multiplications in 11\left(x-2\right)-9.

$$7-\frac{9}{\frac{11x-22-9}{x-2}}=4$$

Combine like terms in 11x-22-9.

$$7-\frac{9}{\frac{11x-31}{x-2}}=4$$

Variable x cannot be equal to 2 since division by zero is not defined. Divide 9 by \frac{11x-31}{x-2} by multiplying 9 by the reciprocal of \frac{11x-31}{x-2}.

$$7-\frac{9\left(x-2\right)}{11x-31}=4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{11x-31}{11x-31}.

$$\frac{7\left(11x-31\right)}{11x-31}-\frac{9\left(x-2\right)}{11x-31}=4$$

Since \frac{7\left(11x-31\right)}{11x-31} and \frac{9\left(x-2\right)}{11x-31} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7\left(11x-31\right)-9\left(x-2\right)}{11x-31}=4$$

Do the multiplications in 7\left(11x-31\right)-9\left(x-2\right).

$$\frac{77x-217-9x+18}{11x-31}=4$$

Combine like terms in 77x-217-9x+18.

$$\frac{68x-199}{11x-31}=4$$

Variable x cannot be equal to \frac{31}{11} since division by zero is not defined. Multiply both sides of the equation by 11x-31.

$$68x-199=4\left(11x-31\right)$$

Use the distributive property to multiply 4 by 11x-31.

$$68x-199=44x-124$$

Subtract 44x from both sides.

$$68x-199-44x=-124$$

Combine 68x and -44x to get 24x.

$$24x-199=-124$$

Add 199 to both sides.

$$24x=-124+199$$

Add -124 and 199 to get 75.

$$24x=75$$

Divide both sides by 24.

$$x=\frac{75}{24}$$

Reduce the fraction \frac{75}{24} to lowest terms by extracting and canceling out 3.

$$x=\frac{25}{8}$$