Here is your inequality:
[tex]z + \frac{1}{8} > \frac{1}{5}[/tex]
You're looking for z. To do that, you need to remove everything on the same side of z. The only thing with z is positive [tex]\frac{1}{8}[/tex] . To remove it, you need to do the opposite of it, which is negative [tex]\frac{1}{8}[/tex], which is the same as subtracting [tex]\frac{1}{8}[/tex]. Subtract:
[tex]z+\frac{1}{8} - \frac{1}{8} > \frac{1}{5} - \frac{1}{8} \\ \\z = \frac{1}{5} - \frac{1}{8}[/tex]
Subtract [tex]\frac{1}{8}[/tex] from [tex]\frac{1}{5}[/tex]. Since they have a different denominator(bottom number in a fraction), change them into fractions with common denominator. To find a common denominator, list the multiples of both numbers and see what is common.
[tex]5 - 5, 10, 15, 20, 25, 30, 35, 40, 45 \\8- 8, 16, 24, 32, 40, 48[/tex]
In the numbers listed above ↑, the only common multiples is 40. That means you need to change both fractions so that they both have a denominator of 40.
[tex]\frac{1 \times 8}{5 \times 8} = \frac{8}{40}[/tex]
[tex]\frac{1 \times 5}{8 \times 5} = \frac{5}{40}[/tex]
Here is your new equation:
[tex]z> \frac{8}{40} - \frac{5}{40}[/tex]
Subtract:
[tex]\frac{8}{40} - \frac{5}{40} = \frac{3}{40} \\\\z> \frac{3}{40}[/tex]
Your answer is z > [tex]\bf \frac{3}{40}[/tex]
If you have any questions, feel free to ask in the comments! :)
GRAPH:
