Question

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

Answer 1

To solve the inequality \( \frac{3}{5} + a \geq -\frac{2}{5} \), we will isolate \( a \).

1. **Subtract \( \frac{3}{5} \) from both sides**:
\[
a \geq -\frac{2}{5} - \frac{3}{5}
\]

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

So, the solution to the inequality is:
\[
a \geq -1
\]

### Part 1 Answer:
- You should enter:
\[
\text{greater than or equals}
\]

### Graphing the Solution:
To graph the solution \( a \geq -1 \):
- Draw a number line.
- Place a solid circle at \( -1 \) to indicate that \( -1 \) is included in the solution.
- Shade the region to the right of \( -1 \) to indicate all values greater than \( -1 \).

### Checking Your Solution:
To check if the solution is correct, you can substitute some values into the original inequality \( \frac{3}{5} + a \geq -\frac{2}{5} \).

- **Test \( a = -1 \)**:
\[
\frac{3}{5} + (-1) = \frac{3}{5} - \frac{5}{5} = -\frac{2}{5} \quad (\text{True, } -\frac{2}{5} \geq -\frac{2}{5})
\]

- **Test \( a = 0 \)**:
\[
\frac{3}{5} + 0 = \frac{3}{5} \quad (\text{True, } \frac{3}{5} \geq -\frac{2}{5})
\]

- **Test \( a = -2 \)**:
\[
\frac{3}{5} + (-2) = \frac{3}{5} - \frac{10}{5} = -\frac{7}{5} \quad (\text{False, } -\frac{7}{5} \geq -\frac{2}{5})
\]

All checks are consistent with our solution, confirming that \( a \geq -1 \) is correct.