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

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

Solve for x

$$x=-\frac{5}{18}\approx -0.277777778$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

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

Combine 5x and -2x to get 3x.

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

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

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

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$3x=-\frac{3}{6}-\frac{2}{6}$$

Since -\frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$3x=\frac{-3-2}{6}$$

Subtract 2 from -3 to get -5.

$$3x=-\frac{5}{6}$$

Divide both sides by 3.

$$x=\frac{-\frac{5}{6}}{3}$$

Express \frac{-\frac{5}{6}}{3} as a single fraction.

$$x=\frac{-5}{6\times 3}$$

Multiply 6 and 3 to get 18.

$$x=\frac{-5}{18}$$

Fraction \frac{-5}{18} can be rewritten as -\frac{5}{18} by extracting the negative sign.

$$x=-\frac{5}{18}$$