Question

Number line has solid circle on the 1 and goes to the right to 10.
Which inequalities is correct?
×-1>0
×+5>6( > is underscored)
× +0.5>( > is underscored) 0.5
× -0.5<( < is underscored) o.5

Answer 1

To determine which inequalities are correct given the number line described (with a solid circle on 1 and extending to the right to 10), we interpret this as meaning that \( x \) can take values from 1 to 10, inclusive.

Now we'll analyze each of the provided inequalities:

1. **\( x - 1 > 0 \)**:
- This implies \( x > 1 \).
- Values of \( x \) can be between 1 and 10, which includes 1 but not greater than 1. Therefore, this inequality is **not correct** as \( x \) can also be 1.

2. **\( x + 5 > 6 \)**:
- This simplifies to \( x > 1 \).
- Similar to the first inequality, the range of \( x \) includes 1. Therefore, it is **not correct** as \( x \) can also be 1.

3. **\( x + 0.5 > 0.5 \)**:
- This simplifies to \( x > 0 \).
- Since the minimum value for \( x \) is 1, this inequality is always satisfied (since 1 is greater than 0). Thus, this inequality is **correct**.

4. **\( x - 0.5 < 0.5 \)**:
- This simplifies to \( x < 1 \).
- Given the range starts at 1 (inclusive), this is **not correct** since \( x \) can be equal to 1.

Thus, the only correct inequality is **\( x + 0.5 > 0.5 \)**.