Question

Solve the inequality. Graph and check your solutions.
minusfive sixths
less thanrminusfive sixths
Question content area bottom
Part 1
r
▼
greater than or equals
less than or equals
less than
greater than
  
enter your response here
​(Simplify your​ answer.)

Answer 1

To solve the inequality you provided, which appears to be:

\[
-\frac{5}{6} < r - \frac{5}{6}
\]

we need to isolate \( r \).

### Step 1: Add \(\frac{5}{6}\) to both sides
\[
-\frac{5}{6} + \frac{5}{6} < r - \frac{5}{6} + \frac{5}{6}
\]

This simplifies to:
\[
0 < r
\]

### Step 2: Rewrite the inequality
This can be rewritten as:
\[
r > 0
\]

### Step 3: Graph the solution
To graph \( r > 0 \), you would draw a number line:

1. Mark the point \(0\) on the number line.
2. Draw an open circle at \(0\) (indicating that \(0\) is not included).
3. Shade the line to the right of \(0\) (indicating all values greater than \(0\)).

### Check the solution
To check the solution \( r > 0 \):

- If we pick a value \(r = 1\) (which is greater than \(0\)):
\[
-\frac{5}{6} < 1 - \frac{5}{6}
\]
\[
-\frac{5}{6} < 1 - \frac{5}{6} \Rightarrow -\frac{5}{6} < \frac{1}{6} \quad \text{(True)}
\]

- If we pick a value \(r = -1\) (which is not greater than \(0\)):
\[
-\frac{5}{6} < -1 - \frac{5}{6}
\]
\[
-\frac{5}{6} < -\frac{6}{6} - \frac{5}{6} \Rightarrow -\frac{5}{6} < -\frac{11}{6} \quad \text{(False)}
\]

### Solution
Thus, the solution is:

\[
r > 0
\]

### Final Answer
The completed inequality is:
\[
r > 0
\]