Solve x+x/2+x/3+2x/3+2x/3+(x-50)+(x-20)

$$x + \frac { x } { 2 } + \frac { x } { 3 } + \frac { 2 x } { 3 } + \frac { 2 x } { 3 } + ( x - 50 ) + ( x - 20 )$$

Evaluate

$$\frac{31x}{6}-70$$

Solution Steps

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

$$\frac{3}{2}x+\frac{x}{3}+\frac{2x}{3}+\frac{2x}{3}+x-50+x-20$$

Combine \frac{3}{2}x and \frac{x}{3} to get \frac{11}{6}x.

$$\frac{11}{6}x+\frac{2x}{3}+\frac{2x}{3}+x-50+x-20$$

Combine \frac{2x}{3} and \frac{2x}{3} to get \frac{2}{3}\times 2x.

$$\frac{11}{6}x+\frac{2}{3}\times 2x+x-50+x-20$$

Combine \frac{11}{6}x and x to get \frac{17}{6}x.

$$\frac{17}{6}x+\frac{2}{3}\times 2x-50+x-20$$

Combine \frac{17}{6}x and x to get \frac{23}{6}x.

$$\frac{23}{6}x+\frac{2}{3}\times 2x-50-20$$

Subtract 20 from -50 to get -70.

$$\frac{23}{6}x+\frac{2}{3}\times 2x-70$$

Express \frac{2}{3}\times 2 as a single fraction.

$$\frac{23}{6}x+\frac{2\times 2}{3}x-70$$

Multiply 2 and 2 to get 4.

$$\frac{23}{6}x+\frac{4}{3}x-70$$

Combine \frac{23}{6}x and \frac{4}{3}x to get \frac{31}{6}x.

$$\frac{31}{6}x-70$$

Factor

$$\frac{31x-420}{6}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{31x-420}{6}$$

Consider 6x+3x+2x+4x+4x+6x-300+6x-120. Multiply and combine like terms.

$$31x-420$$

Rewrite the complete factored expression.

$$\frac{31x-420}{6}$$