To determine which inequality Weston solved, we need to look at the graph on the number line. The closed circle at 1 and the arrow extending to the right toward 10 indicate that the solution includes 1 and all numbers greater than 1.
1. **x + 0.5 ≥ 0.5**
Simplifies to \( x \geq 0 \), which is not correct since the solution starts from 1, not 0.
2. **x + 5 ≥ 6**
Simplifies to \( x \geq 1 \), which matches the graph perfectly because it includes 1 and all numbers greater than 1.
3. **x − 1 > 0**
Simplifies to \( x > 1 \), which does not include the number 1, so it doesn't match the graph since 1 is included (as indicated by the closed circle).
4. **x − 0.5 ≤ 0.5**
Simplifies to \( x \leq 1 \), which does not match the graph because the solution extends to numbers greater than 1.
From this analysis, the correct inequality Weston solved is:
**x + 5 ≥ 6**
This inequality correctly corresponds to the closed circle at 1 and the arrow indicating all numbers greater than or equal to 1.
Use the image to answer the question. A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 1. A line is drawn from 1 toward 10 with an arrow at the end. Weston solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve? (1 point) Responses x+0.5≥0.5 x plus 0.5 greater-than-or-equal-to 0.5 x+5≥6 x plus 5 greater-than-or-equal-to 6 x−1>0 x minus 1 greater-than 0 x−0.5≤0.5
1 answer