Question

Solve the inequality. Graph and check your solutions.
-1/2<r-1/2

Answer 1

To solve the inequality, we will first isolate the variable r on one side of the inequality.

-1/2 < r - 1/2

Adding 1/2 to both sides, we get:
-1/2 + 1/2 < r - 1/2 + 1/2
0 < r

So the solution to the inequality is r > 0.

Now let's graph this inequality on the number line:

0

We shade the region to the right of 0 to represent r > 0.

Finally, let's check a value in that region to see if it satisfies the inequality. Let's choose r = 1.

-1/2 < 1 - 1/2
-1/2 < 1/2 (which is true)

Since the inequality holds for r = 1, we can conclude that the solution to the inequality is r > 0.