Solve 200/xdiv2=180/x+45

$$\frac { 200 } { x } \div 2 = \frac { 180 } { x + 45 }$$

Solve for x

$$x = \frac{225}{4} = 56\frac{1}{4} = 56.25$$

Steps for Solving Linear Equation

Variable x cannot be equal to -45 since division by zero is not defined. Multiply both sides of the equation by 2\left(x+45\right), the least common multiple of 2,x+45.

$$\left(x+45\right)\times \frac{200}{x}=2\times 180$$

Express \left(x+45\right)\times \frac{200}{x} as a single fraction.

$$\frac{\left(x+45\right)\times 200}{x}=2\times 180$$

Multiply 2 and 180 to get 360.

$$\frac{\left(x+45\right)\times 200}{x}=360$$

Use the distributive property to multiply x+45 by 200.

$$\frac{200x+9000}{x}=360$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$200x+9000=360x$$

Subtract 360x from both sides.

$$200x+9000-360x=0$$

Combine 200x and -360x to get -160x.

$$-160x+9000=0$$

Subtract 9000 from both sides. Anything subtracted from zero gives its negation.

$$-160x=-9000$$

Divide both sides by -160.

$$x=\frac{-9000}{-160}$$

Reduce the fraction \frac{-9000}{-160} to lowest terms by extracting and canceling out -40.

$$x=\frac{225}{4}$$