Solve 4-9.45/30-x=9.45-10/x-35

$$\frac{ 4-9.45 }{ 30-x } = \frac{ 9.45-10 }{ x-35 }$$

Solve for x

$$x = \frac{829}{24} = 34\frac{13}{24} \approx 34.541666667$$

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.

$$\left(35-x\right)\left(4-9.45\right)=\left(x-30\right)\left(9.45-10\right)$$

Subtract 9.45 from 4 to get -5.45.

$$\left(35-x\right)\left(-5.45\right)=\left(x-30\right)\left(9.45-10\right)$$

Use the distributive property to multiply 35-x by -5.45.

$$-190.75+5.45x=\left(x-30\right)\left(9.45-10\right)$$

Subtract 10 from 9.45 to get -0.55.

$$-190.75+5.45x=\left(x-30\right)\left(-0.55\right)$$

Use the distributive property to multiply x-30 by -0.55.

$$-190.75+5.45x=-0.55x+16.5$$

Add 0.55x to both sides.

$$-190.75+5.45x+0.55x=16.5$$

Combine 5.45x and 0.55x to get 6x.

$$-190.75+6x=16.5$$

Add 190.75 to both sides.

$$6x=16.5+190.75$$

Add 16.5 and 190.75 to get 207.25.

$$6x=207.25$$

Divide both sides by 6.

$$x=\frac{207.25}{6}$$

Expand \frac{207.25}{6} by multiplying both numerator and the denominator by 100.

$$x=\frac{20725}{600}$$

Reduce the fraction \frac{20725}{600} to lowest terms by extracting and canceling out 25.

$$x=\frac{829}{24}$$