Answer
{15}
Work Step by Step
$\frac{z}{5}$ - $\frac{1}{2}$ = $\frac{z}{6}$
Step 1 : Collect variable terms on one side and constants on the other side.
Add $\frac{1}{2}$ on both the sides
$\frac{z}{5}$ - $\frac{1}{2}$ + $\frac{1}{2}$ = $\frac{z}{6}$ + $\frac{1}{2}$
$\frac{z}{5}$ = $\frac{z}{6}$ + $\frac{1}{2}$
Subtract $\frac{z}{6}$ from both the sides
$\frac{z}{5}$ - $\frac{z}{6}$ = $\frac{z}{6}$ + $\frac{1}{2}$ - $\frac{z}{6}$
$\frac{z}{5}$ - $\frac{z}{6}$ = $\frac{1}{2}$
Step 2 : Multiply both the sides by 30
($\frac{z}{5}$ - $\frac{z}{6}$)*30 = $\frac{1}{2}$*30
$\frac{z}{5}$ * 30 - $\frac{z}{6}$ * 30= $\frac{1}{2}$*30
6z - 5z = 15
Step 3: Add 6z - 5z = z
z = 15
Now we check the proposed solution, 15 , by replacing z with 15 in the original equation.
Step 1: the original equation $\frac{z}{5}$ - $\frac{1}{2}$ = $\frac{z}{6}$
Step2: Substitute 15 for z
$\frac{15}{5}$ - $\frac{1}{2}$ = $\frac{15}{6}$
Step 3: Divide $\frac{15 }{5}$ = 3
3 - $\frac{1}{2}$ = $\frac{15}{6}$
Step 4 : Multiply both the sides by 6
(3 - $\frac{1}{2}$)*6 = $\frac{15}{6}$*6
18 - 3 = 15
Step 5 : Subtract 18 - 3 = 15
15 = 15
Since the check results in true statement, we conclude that the solution set of the given equation is {15}.
