Solve 3x-1/2=5x-4/3

$$3 x - 1 / 2 = 5 x - 4 / 3$$

Solve for x

$$x=\frac{5}{12}\approx 0.416666667$$

Steps for Solving Linear Equation

Subtract 5x from both sides.

$$3x-\frac{1}{2}-5x=-\frac{4}{3}$$

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

$$-2x-\frac{1}{2}=-\frac{4}{3}$$

Add \frac{1}{2} to both sides.

$$-2x=-\frac{4}{3}+\frac{1}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{4}{3} and \frac{1}{2} to fractions with denominator 6.

$$-2x=-\frac{8}{6}+\frac{3}{6}$$

Since -\frac{8}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$-2x=\frac{-8+3}{6}$$

Add -8 and 3 to get -5.

$$-2x=-\frac{5}{6}$$

Divide both sides by -2.

$$x=\frac{-\frac{5}{6}}{-2}$$

Express \frac{-\frac{5}{6}}{-2} as a single fraction.

$$x=\frac{-5}{6\left(-2\right)}$$

Multiply 6 and -2 to get -12.

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

Fraction \frac{-5}{-12} can be simplified to \frac{5}{12} by removing the negative sign from both the numerator and the denominator.

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