Question

Solve the inequality. Graph and check your solutions.
two sevenths plus a greater than or equals minus five sevenths
Question content area bottom
Part 1
a
▼
less than
greater than
greater than or equals
less than or equals
  
enter your response here
​(Simplify your​ answer.)

Answer 1

To solve the inequality \( \frac{2}{7} + a \geq -\frac{5}{7} \), we will isolate \( a \).

1. Start with the inequality:
\[
\frac{2}{7} + a \geq -\frac{5}{7}
\]

2. Subtract \( \frac{2}{7} \) from both sides:
\[
a \geq -\frac{5}{7} - \frac{2}{7}
\]

3. Combine the fractions on the right side:
\[
-\frac{5}{7} - \frac{2}{7} = -\frac{5 + 2}{7} = -\frac{7}{7} = -1
\]

4. The inequality now reads:
\[
a \geq -1
\]

Part 1 - Your answer is:
\[
a \text{ is greater than or equal to } -1
\]

### Graphing the solution
On a number line, we would represent this solution as follows:
- Draw a solid circle at -1 (to indicate that -1 is included in the solution set).
- Shade to the right to indicate all numbers greater than -1.

### Checking your solution
To check:
- Pick a value greater than -1, say \( a = 0 \):
\[
\frac{2}{7} + 0 = \frac{2}{7}
\]
\[
\frac{2}{7} \geq -\frac{5}{7} \text{ (True)}
\]

- Pick a value less than -1, say \( a = -2 \):
\[
\frac{2}{7} - 2 = \frac{2}{7} - \frac{14}{7} = -\frac{12}{7}
\]
\[
-\frac{12}{7} \geq -\frac{5}{7} \text{ (False)}
\]

The solution \( a \geq -1 \) is verified as correct.