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

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

Solve for x

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

Steps for Solving Linear Equation

Subtract 5x from both sides.

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

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

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

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

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

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

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

Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

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

Add 2 and 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.

$$x=\frac{5}{6\left(-3\right)}$$

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.

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