To determine which inequality Weston solved, we need to consider the information provided by the graph:
- 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.
The closed circle at 1 indicates that 1 is included in the solution (which means we are dealing with a "greater than or equal to" or "less than or equal to" condition). The line extending towards 10 with an arrow indicates all numbers greater than 1 are part of the solution.
Given these observations, let's evaluate the given inequalities:
1. \( x + 0.5 \geq 0.5 \)
\[ x + 0.5 \geq 0.5 \]
Subtract 0.5 from both sides:
\[ x \geq 0 \]
This would correspond to a line starting at 0, not 1.
2. \( x + 5 \geq 6 \)
\[ x + 5 \geq 6 \]
Subtract 5 from both sides:
\[ x \geq 1 \]
This matches the graph as it includes 1 and all numbers greater than 1.
3. \( x - 1 > 0 \)
\[ x - 1 > 0 \]
Add 1 to both sides:
\[ x > 1 \]
This does not include 1 itself, so it doesn't match the graph (which includes 1).
4. \( x - 0.5 \leq 0.5 \)
\[ x - 0.5 \leq 0.5 \]
Add 0.5 to both sides:
\[ x \leq 1 \]
This corresponds to numbers less than or equal to 1, which does not match the graph showing numbers greater than or equal to 1.
From the analysis, the inequality that matches the graph is:
\[ x + 5 \geq 6 \]
So, the correct inequality Weston solved is:
\[ x + 5 \geq 6 \]
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