Solve left(100-xright)22.05=left(x-10right)33.6+left(x-10right)4200*0.01

$$\left( 100-x \right) 22.05 = \left( x-10 \right) 33.6+ \left( x-10 \right) 4200 \times 0.01$$

Solve for x

$$x = \frac{940}{31} = 30\frac{10}{31} \approx 30.322580645$$

Steps for Solving Linear Equation

Use the distributive property to multiply 100-x by 22.05.

$$2205-22.05x=\left(x-10\right)\times 33.6+\left(x-10\right)\times 4200\times 0.01$$

Use the distributive property to multiply x-10 by 33.6.

$$2205-22.05x=33.6x-336+\left(x-10\right)\times 4200\times 0.01$$

Multiply 4200 and 0.01 to get 42.

$$2205-22.05x=33.6x-336+\left(x-10\right)\times 42$$

Use the distributive property to multiply x-10 by 42.

$$2205-22.05x=33.6x-336+42x-420$$

Combine 33.6x and 42x to get 75.6x.

$$2205-22.05x=75.6x-336-420$$

Subtract 420 from -336 to get -756.

$$2205-22.05x=75.6x-756$$

Subtract 75.6x from both sides.

$$2205-22.05x-75.6x=-756$$

Combine -22.05x and -75.6x to get -97.65x.

$$2205-97.65x=-756$$

Subtract 2205 from both sides.

$$-97.65x=-756-2205$$

Subtract 2205 from -756 to get -2961.

$$-97.65x=-2961$$

Divide both sides by -97.65.

$$x=\frac{-2961}{-97.65}$$

Expand \frac{-2961}{-97.65} by multiplying both numerator and the denominator by 100.

$$x=\frac{-296100}{-9765}$$

Reduce the fraction \frac{-296100}{-9765} to lowest terms by extracting and canceling out -315.

$$x=\frac{940}{31}$$