Solve 100+0.9(x-100)=50+0.95(x-50)

$$100+0.9(x-100)=50+0.95(x-50)$$

Solve for x

$$x=150$$

Steps for Solving Linear Equation

Use the distributive property to multiply 0.9 by x-100.

$$100+0.9x-90=50+0.95\left(x-50\right)$$

Subtract 90 from 100 to get 10.

$$10+0.9x=50+0.95\left(x-50\right)$$

Use the distributive property to multiply 0.95 by x-50.

$$10+0.9x=50+0.95x-47.5$$

Subtract 47.5 from 50 to get 2.5.

$$10+0.9x=2.5+0.95x$$

Subtract 0.95x from both sides.

$$10+0.9x-0.95x=2.5$$

Combine 0.9x and -0.95x to get -0.05x.

$$10-0.05x=2.5$$

Subtract 10 from both sides.

$$-0.05x=2.5-10$$

Subtract 10 from 2.5 to get -7.5.

$$-0.05x=-7.5$$

Divide both sides by -0.05.

$$x=\frac{-7.5}{-0.05}$$

Expand \frac{-7.5}{-0.05} by multiplying both numerator and the denominator by 100.

$$x=\frac{-750}{-5}$$

Divide -750 by -5 to get 150.

$$x=150$$