#### Answer

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

#### Work Step by Step

1. The first step we want to take is to clear the fractions in this linear equation. To clear fractions, we want to use the distributive property and distribute the least common denominator. To find the least common denominator we want to list the multiples of each number in the denominators involved until we find the first multiple that each denominator has in common. This is called the least common denominator.
factors of 6: 6, 12, 18, 24, ....
factors of 3: 3, 6, 9, 12,....
The smallest number these two lists have in common is 6. We will use this number to distribute to the entire equation and clear the fractions.
*NOTE: You could use 12 or another number they have in common but that will create larger numbers to work with in the solving process.
$\frac{5}{6}x - 2x +\frac{4}{3} = \frac{5}{3}$
$6(\frac{5}{6}x - 2x +\frac{4}{3} = \frac{5}{3})$
$5x - 12x + 8 = 10$
2. Next, we want to combine the like terms 5x and -12x.
$-7x + 8 = 10$
3. Next, subtract 8 from both sides of the equation to isolate the variable.
$-7x = 2$
4. And finally, divide both sides by -7 to solve for x.
$x = -\frac{2}{7}$