Solve 4-6/30-x=6-10/x-35

$$\frac{ 4-6 }{ 30-x } = \frac{ 6-10 }{ x-35 }$$

Solve for x

$$x = \frac{95}{3} = 31\frac{2}{3} \approx 31.666666667$$

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.

$$\left(35-x\right)\left(4-6\right)=\left(x-30\right)\left(6-10\right)$$

Subtract 6 from 4 to get -2.

$$\left(35-x\right)\left(-2\right)=\left(x-30\right)\left(6-10\right)$$

Use the distributive property to multiply 35-x by -2.

$$-70+2x=\left(x-30\right)\left(6-10\right)$$

Subtract 10 from 6 to get -4.

$$-70+2x=\left(x-30\right)\left(-4\right)$$

Use the distributive property to multiply x-30 by -4.

$$-70+2x=-4x+120$$

Add 4x to both sides.

$$-70+2x+4x=120$$

Combine 2x and 4x to get 6x.

$$-70+6x=120$$

Add 70 to both sides.

$$6x=120+70$$

Add 120 and 70 to get 190.

$$6x=190$$

Divide both sides by 6.

$$x=\frac{190}{6}$$

Reduce the fraction \frac{190}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{95}{3}$$