Solve 2x+1/3(100-x)=100

$$2 x + \frac { 1 } { 3 } ( 100 - x ) = 100$$

Solve for x

$$x=40$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by 100-x.

$$2x+\frac{1}{3}\times 100+\frac{1}{3}\left(-1\right)x=100$$

Multiply \frac{1}{3} and 100 to get \frac{100}{3}.

$$2x+\frac{100}{3}+\frac{1}{3}\left(-1\right)x=100$$

Multiply \frac{1}{3} and -1 to get -\frac{1}{3}.

$$2x+\frac{100}{3}-\frac{1}{3}x=100$$

Combine 2x and -\frac{1}{3}x to get \frac{5}{3}x.

$$\frac{5}{3}x+\frac{100}{3}=100$$

Subtract \frac{100}{3} from both sides.

$$\frac{5}{3}x=100-\frac{100}{3}$$

Convert 100 to fraction \frac{300}{3}.

$$\frac{5}{3}x=\frac{300}{3}-\frac{100}{3}$$

Since \frac{300}{3} and \frac{100}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}x=\frac{300-100}{3}$$

Subtract 100 from 300 to get 200.

$$\frac{5}{3}x=\frac{200}{3}$$

Multiply both sides by \frac{3}{5}, the reciprocal of \frac{5}{3}.

$$x=\frac{200}{3}\times \frac{3}{5}$$

Multiply \frac{200}{3} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{200\times 3}{3\times 5}$$

Cancel out 3 in both numerator and denominator.

$$x=\frac{200}{5}$$

Divide 200 by 5 to get 40.

$$x=40$$