Solve the inequality. Graph and check your solutions.
- 4/5 <r - 4/5
r
To solve the inequality:
-4/5 < r - 4/5
Add 4/5 to both sides to isolate r:
-4/5 + 4/5 < r - 4/5 + 4/5
0 < r
The solution to the inequality is r > 0.
To graph this inequality on a number line, we represent the solution as a shaded region to the right of 0:
-----|-------------|-----------------|
-3 0
The shaded region represents all the values of r that are greater than 0.
To check the solution, we can choose a value that is greater than 0, such as r = 1, and substitute it into the original inequality:
-4/5 < 1 - 4/5
-4/5 < 5/5 - 4/5
-4/5 < 1/5
Since -4/5 is less than 1/5, the inequality holds true. Hence, the solution r > 0 is correct.