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

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

Solve for x

$$x=-\frac{16}{33}\approx -0.484848485$$

Steps for Solving Linear Equation

Subtract \frac{1}{2}x from both sides.

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

Combine -5x and -\frac{1}{2}x to get -\frac{11}{2}x.

$$\frac{1}{3}-\frac{11}{2}x=3$$

Subtract \frac{1}{3} from both sides.

$$-\frac{11}{2}x=3-\frac{1}{3}$$

Convert 3 to fraction \frac{9}{3}.

$$-\frac{11}{2}x=\frac{9}{3}-\frac{1}{3}$$

Since \frac{9}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{11}{2}x=\frac{9-1}{3}$$

Subtract 1 from 9 to get 8.

$$-\frac{11}{2}x=\frac{8}{3}$$

Multiply both sides by -\frac{2}{11}, the reciprocal of -\frac{11}{2}.

$$x=\frac{8}{3}\left(-\frac{2}{11}\right)$$

Multiply \frac{8}{3} times -\frac{2}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{8\left(-2\right)}{3\times 11}$$

Do the multiplications in the fraction \frac{8\left(-2\right)}{3\times 11}.

$$x=\frac{-16}{33}$$

Fraction \frac{-16}{33} can be rewritten as -\frac{16}{33} by extracting the negative sign.

$$x=-\frac{16}{33}$$