Solve 10-18/35-x=18-30/x-40

$$\frac{ 10-18 }{ 35-x } = \frac{ 18-30 }{ x-40 }$$

Solve for x

$$x=37$$

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.

$$\left(40-x\right)\left(10-18\right)=\left(x-35\right)\left(18-30\right)$$

Subtract 18 from 10 to get -8.

$$\left(40-x\right)\left(-8\right)=\left(x-35\right)\left(18-30\right)$$

Use the distributive property to multiply 40-x by -8.

$$-320+8x=\left(x-35\right)\left(18-30\right)$$

Subtract 30 from 18 to get -12.

$$-320+8x=\left(x-35\right)\left(-12\right)$$

Use the distributive property to multiply x-35 by -12.

$$-320+8x=-12x+420$$

Add 12x to both sides.

$$-320+8x+12x=420$$

Combine 8x and 12x to get 20x.

$$-320+20x=420$$

Add 320 to both sides.

$$20x=420+320$$

Add 420 and 320 to get 740.

$$20x=740$$

Divide both sides by 20.

$$x=\frac{740}{20}$$

Divide 740 by 20 to get 37.

$$x=37$$