Solve 10-13.8/35-x=13.8-30/x-40

$$\frac{ 10-13.8 }{ 35-x } = \frac{ 13.8-30 }{ x-40 }$$

Solve for x

$$x=35.95$$

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.

$$\left(40-x\right)\left(10-13.8\right)=\left(x-35\right)\left(13.8-30\right)$$

Subtract 13.8 from 10 to get -3.8.

$$\left(40-x\right)\left(-3.8\right)=\left(x-35\right)\left(13.8-30\right)$$

Use the distributive property to multiply 40-x by -3.8.

$$-152+3.8x=\left(x-35\right)\left(13.8-30\right)$$

Subtract 30 from 13.8 to get -16.2.

$$-152+3.8x=\left(x-35\right)\left(-16.2\right)$$

Use the distributive property to multiply x-35 by -16.2.

$$-152+3.8x=-16.2x+567$$

Add 16.2x to both sides.

$$-152+3.8x+16.2x=567$$

Combine 3.8x and 16.2x to get 20x.

$$-152+20x=567$$

Add 152 to both sides.

$$20x=567+152$$

Add 567 and 152 to get 719.

$$20x=719$$

Divide both sides by 20.

$$x=\frac{719}{20}$$