Question
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 minus 0.5 less-than-or-equal-to 0.5
x−1>0
x minus 1 greater-than 0
x+5≥6
x plus 5 greater-than-or-equal-to 6
x+0.5≥0.5
x plus 0.5 greater-than-or-equal-to 0.5
(1 point)
Responses
x−0.5≤0.5
x minus 0.5 less-than-or-equal-to 0.5
x−1>0
x minus 1 greater-than 0
x+5≥6
x plus 5 greater-than-or-equal-to 6
x+0.5≥0.5
x plus 0.5 greater-than-or-equal-to 0.5
Answers
GPT-4o mini
To determine which inequality Weston solved based on the solution represented on a number line, we need to consider the intervals and endpoints indicated by each inequality.
1. \( x - 0.5 \leq 0.5 \):
- Solving: \( x \leq 1 \)
- This would include all values less than or equal to 1, represented on the number line with a closed dot at 1 extending left.
2. \( x - 1 > 0 \):
- Solving: \( x > 1 \)
- This would include all values greater than 1, represented on the number line with an open dot at 1 extending right.
3. \( x + 5 \geq 6 \):
- Solving: \( x \geq 1 \)
- This would include all values greater than or equal to 1, represented on the number line with a closed dot at 1 extending right.
4. \( x + 0.5 \geq 0.5 \):
- Solving: \( x \geq 0 \)
- This would include all values greater than or equal to 0, represented on the number line with a closed dot at 0 extending right.
To identify which inequality Weston solved, we would ideally need a description of the graph he produced (closed/open dots, direction of shading, etc.). However, based on the typical inequalities:
- If the graph shows a closed dot at a particular point with shading to the left, it corresponds to the first inequality.
- If it shows an open dot at a point with shading to the right, it corresponds to the second inequality.
- If it shows a closed dot at a point with shading to the right, it corresponds to the third inequality.
- If it shows a closed dot at 0 with shading to the right, it corresponds to the fourth inequality.
Without the specific description of the graph, it’s difficult to select the specific one Weston solved. However, each inequality corresponds to a certain graph format as described above. If you provide a description of the number line graph, I can help you identify which inequality Weston solved!
1. \( x - 0.5 \leq 0.5 \):
- Solving: \( x \leq 1 \)
- This would include all values less than or equal to 1, represented on the number line with a closed dot at 1 extending left.
2. \( x - 1 > 0 \):
- Solving: \( x > 1 \)
- This would include all values greater than 1, represented on the number line with an open dot at 1 extending right.
3. \( x + 5 \geq 6 \):
- Solving: \( x \geq 1 \)
- This would include all values greater than or equal to 1, represented on the number line with a closed dot at 1 extending right.
4. \( x + 0.5 \geq 0.5 \):
- Solving: \( x \geq 0 \)
- This would include all values greater than or equal to 0, represented on the number line with a closed dot at 0 extending right.
To identify which inequality Weston solved, we would ideally need a description of the graph he produced (closed/open dots, direction of shading, etc.). However, based on the typical inequalities:
- If the graph shows a closed dot at a particular point with shading to the left, it corresponds to the first inequality.
- If it shows an open dot at a point with shading to the right, it corresponds to the second inequality.
- If it shows a closed dot at a point with shading to the right, it corresponds to the third inequality.
- If it shows a closed dot at 0 with shading to the right, it corresponds to the fourth inequality.
Without the specific description of the graph, it’s difficult to select the specific one Weston solved. However, each inequality corresponds to a certain graph format as described above. If you provide a description of the number line graph, I can help you identify which inequality Weston solved!