Question

Choose the correct solution and graph for the inequality

Answer 1

Here is your inequality:

$z + \frac{1}{8} > \frac{1}{5}$

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 $\frac{1}{8}$ . To remove it, you need to do the opposite of it, which is negative $\frac{1}{8}$, which is the same as subtracting $\frac{1}{8}$. Subtract:

$z+\frac{1}{8} - \frac{1}{8} > \frac{1}{5} - \frac{1}{8} \\ \\z = \frac{1}{5} - \frac{1}{8}$

Subtract $\frac{1}{8}$ from $\frac{1}{5}$. 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.

$5 - 5, 10, 15, 20, 25, 30, 35, 40, 45 \\8- 8, 16, 24, 32, 40, 48$

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.

$\frac{1 \times 8}{5 \times 8} = \frac{8}{40}$

$\frac{1 \times 5}{8 \times 5} = \frac{5}{40}$

Here is your new equation:

$z> \frac{8}{40} - \frac{5}{40}$

Subtract:

$\frac{8}{40} - \frac{5}{40} = \frac{3}{40} \\\\z> \frac{3}{40}$

Your answer is z > $\bf \frac{3}{40}$

If you have any questions, feel free to ask in the comments! :)

GRAPH: