Answer
{24}
Work Step by Step
20 - $\frac{z}{3}$ = $\frac{z}{2}$
Step 1 : Collect variable terms on one side and constants on the other side.
Add $\frac{z}{3}$ on both the sides
20 - $\frac{z}{3}$ + $\frac{z}{3}$= $\frac{z}{2}$ + $\frac{z}{3}$
20 = $\frac{z}{2}$ + $\frac{z}{3}$
or $\frac{z}{2}$ + $\frac{z}{3}$ = 20
Step 2 : Multiply both the sides by 6
($\frac{z}{2}$ + $\frac{z}{3}$ )* 6= 20* 6
$\frac{z}{2}$ * 6+ $\frac{z}{3}$ * 6= 20* 6
3z + 2z = 120
Step 3: Add 3z + 2z = (3+2 )z = 5z
5z = 120
Step 4: Divide both the sides by 5
$\frac{5z}{5}$ = $\frac{120}{5}$
z = 24
Now we check the proposed solution, 24 , by replacing z with 24 in the original equation.
Step 1: the original equation 20 - $\frac{z}{3}$ = $\frac{z}{2}$
Step2: Substitute 24 for z
20 - $\frac{24}{3}$ = $\frac{24}{2}$
Step 3: Divide $\frac{24}{3}$ = 8, $\frac{24}{2}$ = 12
20 - 8 = 12
Step 4 : Subtract 20 -8 =12
12 = 12
Since the check results in true statement, we conclude that the solution set of the given equation is {24}.
