Solve 90-x/x-81=9/2

$$\frac { 90 - x } { x - 81 } = \frac { 9 } { 2 }$$

Solve for x

$$x = \frac{909}{11} = 82\frac{7}{11} \approx 82.636363636$$

Steps for Solving Linear Equation

Variable x cannot be equal to 81 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-81\right), the least common multiple of x-81,2.

$$2\left(90-x\right)=9\left(x-81\right)$$

Use the distributive property to multiply 2 by 90-x.

$$180-2x=9\left(x-81\right)$$

Use the distributive property to multiply 9 by x-81.

$$180-2x=9x-729$$

Subtract 9x from both sides.

$$180-2x-9x=-729$$

Combine -2x and -9x to get -11x.

$$180-11x=-729$$

Subtract 180 from both sides.

$$-11x=-729-180$$

Subtract 180 from -729 to get -909.

$$-11x=-909$$

Divide both sides by -11.

$$x=\frac{-909}{-11}$$

Fraction \frac{-909}{-11} can be simplified to \frac{909}{11} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{909}{11}$$