Solve 4-5/30-x=5-10/x-35

$$\frac{ 4-5 }{ 30-x } = \frac{ 5-10 }{ x-35 }$$

Solve for x

$$x = \frac{185}{6} = 30\frac{5}{6} \approx 30.833333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 30,35 since division by zero is not defined. Multiply both sides of the equation by \left(x-35\right)\left(x-30\right), the least common multiple of 30-x,x-35.

$$\left(35-x\right)\left(4-5\right)=\left(x-30\right)\left(5-10\right)$$

Subtract 5 from 4 to get -1.

$$\left(35-x\right)\left(-1\right)=\left(x-30\right)\left(5-10\right)$$

Use the distributive property to multiply 35-x by -1.

$$-35+x=\left(x-30\right)\left(5-10\right)$$

Subtract 10 from 5 to get -5.

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

Use the distributive property to multiply x-30 by -5.

$$-35+x=-5x+150$$

Add 5x to both sides.

$$-35+x+5x=150$$

Combine x and 5x to get 6x.

$$-35+6x=150$$

Add 35 to both sides.

$$6x=150+35$$

Add 150 and 35 to get 185.

$$6x=185$$

Divide both sides by 6.

$$x=\frac{185}{6}$$