Solve 328.5-108/x-180=283.5-108/450-180

$$\frac { 328.5 - 108 } { x - 180 } = \frac { 283.5 - 108 } { 450 - 180 }$$

Solve for x

$$x = \frac{6750}{13} = 519\frac{3}{13} \approx 519.230769231$$

Steps for Solving Linear Equation

Variable x cannot be equal to 180 since division by zero is not defined. Multiply both sides of the equation by x-180.

$$328.5-108=\left(\frac{1}{270}x-\frac{2}{3}\right)\left(283.5-108\right)$$

Subtract 108 from 328.5 to get 220.5.

$$220.5=\left(\frac{1}{270}x-\frac{2}{3}\right)\left(283.5-108\right)$$

Subtract 108 from 283.5 to get 175.5.

$$220.5=\left(\frac{1}{270}x-\frac{2}{3}\right)\times 175.5$$

Use the distributive property to multiply \frac{1}{270}x-\frac{2}{3} by 175.5.

$$220.5=\frac{13}{20}x-117$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{13}{20}x-117=220.5$$

Add 117 to both sides.

$$\frac{13}{20}x=220.5+117$$

Add 220.5 and 117 to get 337.5.

$$\frac{13}{20}x=337.5$$

Multiply both sides by \frac{20}{13}, the reciprocal of \frac{13}{20}.

$$x=337.5\times \frac{20}{13}$$

Multiply 337.5 and \frac{20}{13} to get \frac{6750}{13}.

$$x=\frac{6750}{13}$$