Solve 10-15/35-x=15-30/x-40

$$\frac{ 10-15 }{ 35-x } = \frac{ 15-30 }{ x-40 }$$

Solve for x

$$x = \frac{145}{4} = 36\frac{1}{4} = 36.25$$

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.

$$\left(40-x\right)\left(10-15\right)=\left(x-35\right)\left(15-30\right)$$

Subtract 15 from 10 to get -5.

$$\left(40-x\right)\left(-5\right)=\left(x-35\right)\left(15-30\right)$$

Use the distributive property to multiply 40-x by -5.

$$-200+5x=\left(x-35\right)\left(15-30\right)$$

Subtract 30 from 15 to get -15.

$$-200+5x=\left(x-35\right)\left(-15\right)$$

Use the distributive property to multiply x-35 by -15.

$$-200+5x=-15x+525$$

Add 15x to both sides.

$$-200+5x+15x=525$$

Combine 5x and 15x to get 20x.

$$-200+20x=525$$

Add 200 to both sides.

$$20x=525+200$$

Add 525 and 200 to get 725.

$$20x=725$$

Divide both sides by 20.

$$x=\frac{725}{20}$$

Reduce the fraction \frac{725}{20} to lowest terms by extracting and canceling out 5.

$$x=\frac{145}{4}$$