Answer
{1}
Work Step by Step
$\frac{x}{3}$ + $\frac{x}{2}$ =$\frac{5}{6}$
Step 1 : Multiply both the sides by 6
($\frac{x}{3}$ + $\frac{x}{2}$)* 6 =$\frac{5}{6}$ * 6
Solve
$\frac{x}{3}$ * 6 + $\frac{x}{2}$ * 6=$\frac{5}{6}$*6
2x + 3x = 5
Step 2 : Add 2x +3x = (2+3)x = 5x
5x = 5
Step 3: Divide both the sides by 5
$\frac{5x}{5}$ = $\frac{5}{5}$
x = 1
Now we check the proposed solution, 1 , by replacing x with 1 in the original equation.
Step 1: the original equation $\frac{x}{3}$ + $\frac{x}{2}$ =$\frac{5}{6}$
Step2: Substitute 1 for x
$\frac{1}{3}$ + $\frac{1}{2}$ =$\frac{5}{6}$
Step 3: Multiply both sides by 6
$\frac{1}{3}$*6 + $\frac{1}{2}$*6 =$\frac{5}{6}$*6
Simplify
2+3 = 5
Step 4 : Add 2+3 = 5
5 = 5
Since the check results in true statement, we conclude that the solution set of the given equation is {1}.
