Solve 3/5x-2=x+1/3

$$\frac { 3 } { 5 } x - 2 = x + \frac { 1 } { 3 }$$

Solve for x

$$x = -\frac{35}{6} = -5\frac{5}{6} \approx -5.833333333$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$\frac{3}{5}x-2-x=\frac{1}{3}$$

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

$$-\frac{2}{5}x-2=\frac{1}{3}$$

Add 2 to both sides.

$$-\frac{2}{5}x=\frac{1}{3}+2$$

Convert 2 to fraction \frac{6}{3}.

$$-\frac{2}{5}x=\frac{1}{3}+\frac{6}{3}$$

Since \frac{1}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

$$-\frac{2}{5}x=\frac{1+6}{3}$$

Add 1 and 6 to get 7.

$$-\frac{2}{5}x=\frac{7}{3}$$

Multiply both sides by -\frac{5}{2}, the reciprocal of -\frac{2}{5}.

$$x=\frac{7}{3}\left(-\frac{5}{2}\right)$$

Multiply \frac{7}{3} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\left(-5\right)}{3\times 2}$$

Do the multiplications in the fraction \frac{7\left(-5\right)}{3\times 2}.

$$x=\frac{-35}{6}$$

Fraction \frac{-35}{6} can be rewritten as -\frac{35}{6} by extracting the negative sign.

$$x=-\frac{35}{6}$$