Solve 10-20/35-x=20-30/x-40

$$\frac{ 10-20 }{ 35-x } = \frac{ 20-30 }{ x-40 }$$

Solve for x

$$x = \frac{75}{2} = 37\frac{1}{2} = 37.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 35,40 since division by zero is not defined. Multiply both sides of the equation by \left(x-40\right)\left(x-35\right), the least common multiple of 35-x,x-40.

$$\left(40-x\right)\left(10-20\right)=\left(x-35\right)\left(20-30\right)$$

Subtract 20 from 10 to get -10.

$$\left(40-x\right)\left(-10\right)=\left(x-35\right)\left(20-30\right)$$

Use the distributive property to multiply 40-x by -10.

$$-400+10x=\left(x-35\right)\left(20-30\right)$$

Subtract 30 from 20 to get -10.

$$-400+10x=\left(x-35\right)\left(-10\right)$$

Use the distributive property to multiply x-35 by -10.

$$-400+10x=-10x+350$$

Add 10x to both sides.

$$-400+10x+10x=350$$

Combine 10x and 10x to get 20x.

$$-400+20x=350$$

Add 400 to both sides.

$$20x=350+400$$

Add 350 and 400 to get 750.

$$20x=750$$

Divide both sides by 20.

$$x=\frac{750}{20}$$

Reduce the fraction \frac{750}{20} to lowest terms by extracting and canceling out 10.

$$x=\frac{75}{2}$$