Solve 30-37/40-x=37-50/x-45

$$\frac{ 30-37 }{ 40-x } = \frac{ 37-50 }{ x-45 }$$

Solve for x

$$x = \frac{167}{4} = 41\frac{3}{4} = 41.75$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 40,45 since division by zero is not defined. Multiply both sides of the equation by \left(x-45\right)\left(x-40\right), the least common multiple of 40-x,x-45.

$$\left(45-x\right)\left(30-37\right)=\left(x-40\right)\left(37-50\right)$$

Subtract 37 from 30 to get -7.

$$\left(45-x\right)\left(-7\right)=\left(x-40\right)\left(37-50\right)$$

Use the distributive property to multiply 45-x by -7.

$$-315+7x=\left(x-40\right)\left(37-50\right)$$

Subtract 50 from 37 to get -13.

$$-315+7x=\left(x-40\right)\left(-13\right)$$

Use the distributive property to multiply x-40 by -13.

$$-315+7x=-13x+520$$

Add 13x to both sides.

$$-315+7x+13x=520$$

Combine 7x and 13x to get 20x.

$$-315+20x=520$$

Add 315 to both sides.

$$20x=520+315$$

Add 520 and 315 to get 835.

$$20x=835$$

Divide both sides by 20.

$$x=\frac{835}{20}$$

Reduce the fraction \frac{835}{20} to lowest terms by extracting and canceling out 5.

$$x=\frac{167}{4}$$