Solve 4x/3-x-2/5=x

$$\frac{ 4x }{ 3 } - \frac{ x-2 }{ 5 } =x$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{4x}{3} times \frac{5}{5}. Multiply \frac{x-2}{5} times \frac{3}{3}.

$$\frac{5\times 4x}{15}-\frac{3\left(x-2\right)}{15}=x$$

Since \frac{5\times 4x}{15} and \frac{3\left(x-2\right)}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 4x-3\left(x-2\right)}{15}=x$$

Do the multiplications in 5\times 4x-3\left(x-2\right).

$$\frac{20x-3x+6}{15}=x$$

Combine like terms in 20x-3x+6.

$$\frac{17x+6}{15}=x$$

Divide each term of 17x+6 by 15 to get \frac{17}{15}x+\frac{2}{5}.

$$\frac{17}{15}x+\frac{2}{5}=x$$

Subtract x from both sides.

$$\frac{17}{15}x+\frac{2}{5}-x=0$$

Combine \frac{17}{15}x and -x to get \frac{2}{15}x.

$$\frac{2}{15}x+\frac{2}{5}=0$$

Subtract \frac{2}{5} from both sides. Anything subtracted from zero gives its negation.

$$\frac{2}{15}x=-\frac{2}{5}$$

Multiply both sides by \frac{15}{2}, the reciprocal of \frac{2}{15}.

$$x=-\frac{2}{5}\times \frac{15}{2}$$

Multiply -\frac{2}{5} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-2\times 15}{5\times 2}$$

Do the multiplications in the fraction \frac{-2\times 15}{5\times 2}.

$$x=\frac{-30}{10}$$

Divide -30 by 10 to get -3.

$$x=-3$$