Solve 7x/5/11frac{2{3}}=7x/5+x/20

$$\frac { \frac { 7 x } { 5 } } { 11 \frac { 2 } { 3 } } = \frac { \frac { 7 x } { 5 } + x } { 20 }$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Short Solution Steps

Multiply both sides of the equation by 20.

$$\frac{12}{7}\times \frac{7x}{5}=\frac{7x}{5}+x$$

Multiply \frac{12}{7} times \frac{7x}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 7x}{7\times 5}=\frac{7x}{5}+x$$

Cancel out 7 in both numerator and denominator.

$$\frac{12x}{5}=\frac{7x}{5}+x$$

Subtract \frac{7x}{5} from both sides.

$$\frac{12x}{5}-\frac{7x}{5}=x$$

Since \frac{12x}{5} and \frac{7x}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12x-7x}{5}=x$$

Combine like terms in 12x-7x.

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

Cancel out 5 and 5.

$$x=x$$

Subtract x from both sides.

$$x-x=0$$

Combine x and -x to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Short Solution Steps

Multiply both sides of the equation by 20.

$$\frac{12}{7}\times \frac{7x}{5}=\frac{7x}{5}+x$$

Multiply \frac{12}{7} times \frac{7x}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 7x}{7\times 5}=\frac{7x}{5}+x$$

Cancel out 7 in both numerator and denominator.

$$\frac{12x}{5}=\frac{7x}{5}+x$$

Subtract \frac{7x}{5} from both sides.

$$\frac{12x}{5}-\frac{7x}{5}=x$$

Since \frac{12x}{5} and \frac{7x}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12x-7x}{5}=x$$

Combine like terms in 12x-7x.

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

Cancel out 5 and 5.

$$x=x$$

Subtract x from both sides.

$$x-x=0$$

Combine x and -x to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$