10. drag the word description for an inequality to the correct start/endpoint.
is not equal to
is less than
is at least
is no less than
point / solid dot
answer by dragging items here
open dot / bubble
answer by dragging items here

Question

10. drag the word description for an inequality to the correct start/endpoint.
 is not equal to
 is less than
 is at least
 is no less than
 point / solid dot
 answer by dragging items here
 open dot / bubble
 answer by dragging items here

Accepted Answer

# Brief Explanations: - For a solid dot (point) in inequality graphing, the inequality includes the endpoint. "is at least" ($\geq$) and "is no less than" ($\geq$) and also "is equal to" related, but here "is at least" (meaning $\geq$) and "is no less than" (same as $\geq$) and actually "is equal to" - but in the options, "is at least" and "is no less than" correspond to including the endpoint (solid dot). Wait, correction: the solid dot (point) is used when the inequality is "greater than or equal to" ($\geq$) or "less than or equal to" ($\leq$), which correspond to "is at least" ($\geq$) and "is at most" (but here we have "is at least" and "is no less than" (same as $\geq$), and "is not equal to" ($ eq$) and "is less than" ($<$) use open dot. Wait, let's re-express: - Solid Dot (Point): Used when the inequality includes the endpoint, i.e., for $\geq$ (is at least, is no less than) or $\leq$ (but here we don't have $\leq$). Wait, the options: "is at least" means $\geq$ (includes the endpoint), "is no less than" also means $\geq$ (includes the endpoint). Wait, no, "is less than" is $<$ (does not include, open dot), "is not equal to" is $ eq$ (open dot). Wait, maybe I mixed up. Let's recall: - In number line graphs: - Solid dot (filled circle): the value is included (inequality is $\leq$ or $\geq$). - Open dot (unfilled circle): the value is not included (inequality is $<$ or $>$ or $ eq$). So: - "is at least" means $\geq$ (include the endpoint) → solid dot. - "is no less than" means $\geq$ (include the endpoint) → solid dot. - "is less than" means $<$ (do not include) → open dot. - "is not equal to" means $ eq$ (do not include) → open dot. Wait, but the left side has four options: "is not equal to", "is less than", "is at least", "is no less than". The right side has two boxes: Solid Dot (Point) and Open Dot (Bubble). So: Solid Dot (Point) should have the inequalities that include the endpoint: "is at least" ($\geq$) and "is no less than" ($\geq$). Wait, but the problem says "drag the word description" (each description is a separate item). Wait, the left has four items: each is a separate draggable. So: - Solid Dot (Point) (includes endpoint): "is at least" (since $\geq$ includes the endpoint), "is no less than" (same as $\geq$ includes the endpoint). Wait, but maybe "is at least" and "is no less than" are for solid dot, and "is less than" and "is not equal to" are for open dot. Wait, let's list: Inequality symbols and their dot types: - $<$ (is less than): open dot (not included) - $>$ (is greater than): open dot (not included) - $ eq$ (is not equal to): open dot (not included) - $\leq$ (is at most): solid dot (included) - $\geq$ (is at least, is no less than): solid dot (included) So: Solid Dot (Point) (include endpoint): "is at least", "is no less than" Open Dot (Bubble) (do not include): "is less than", "is not equal to" Wait, but the left has four items: four descriptions. So: Solid Dot (Point) box: drag "is at least" and "is no less than" (but wait, the problem says "drag the word description for an inequality to the correct start/endpoint" – maybe each description is a single item, so: Wait, maybe the problem is that each of the four left items is a single description, and we need to drag each to either Solid Dot or Open Dot. So: - "is at least" → Solid Dot (because $\geq$ includes the endpoint) - "is no less than" → Solid Dot (because $\geq$ includes the endpoint) - "is less than" → Open Dot (because $<$ does not include) - "is not equal to" → Open Dot (because $ eq$ does not include) But let's check the options again. The left column has four draggable items: 1. is not equal to 2. is less than 3. is at least 4. is no less than Right column: - Point / Solid Dot (green filled circle) - Open Dot / Bubble (green open circle) So: For Solid Dot (Point): - "is at least" (since $\geq$ includes the endpoint) - "is no less than" (since $\geq$ includes the endpoint) For Open Dot (Bubble): - "is less than" (since $<$ does not include) - "is not equal to" (since $ eq$ does not include) But maybe the problem expects: Solid Dot (Point) gets "is at least" and "is no less than" (but wait, maybe I made a mistake. Wait, "is at least" is $\geq$, "is no less than" is $\geq$, "is less than" is $<$, "is not equal to" is $ eq$. So: Solid Dot (Point) (include the endpoint): "is at least", "is no less than" Open Dot (Bubble) (do not include): "is less than", "is not equal to" But the problem says "drag the word description for an inequality to the correct start/endpoint" – so each description is a separate drag. So: - "is at least" → Solid Dot - "is no less than" → Solid Dot - "is less than" → Open Dot - "is not equal to" → Open Dot But maybe the options are: Wait, the left has four: "is not equal to", "is less than", "is at least", "is no less than". So: Solid Dot (Point) (filled circle) corresponds to inequalities where the endpoint is included (≥ or ≤). So "is at least" (≥) and "is no less than" (≥) go to Solid Dot. Open Dot (Bubble) (unfilled circle) corresponds to inequalities where the endpoint is not included (<, >, ≠). So "is less than" (<) and "is not equal to" (≠) go to Open Dot. So the correct drags are: - Solid Dot (Point): "is at least", "is no less than" - Open Dot (Bubble): "is less than", "is not equal to" But the problem might have a different way, but based on standard number line graphing: - Solid Dot (include endpoint): "is at least" (≥), "is no less than" (≥) - Open Dot (exclude endpoint): "is less than" (<), "is not equal to" (≠) So the answer is: Point / Solid Dot (filled circle) should have "is at least" and "is no less than". Open Dot / Bubble (unfilled circle) should have "is less than" and "is not equal to". But since the problem is a drag-and-drop, the answer would be: - Drag "is at least" and "is no less than" to "Point / Solid Dot". - Drag "is less than" and "is not equal to" to "Open Dot / Bubble". But maybe the options are: Wait, the left has four items: 1. is not equal to → Open Dot 2. is less than → Open Dot 3. is at least → Solid Dot 4. is no less than → Solid Dot So the correct mapping is: Point / Solid Dot: "is at least", "is no less than" Open Dot / Bubble: "is not equal to", "is less than" # Answer: - Point / Solid Dot (filled circle) should have: "is at least", "is no less than" - Open Dot / Bubble (unfilled circle) should have: "is not equal to", "is less than" (To drag: move "is at least" and "is no less than" to the "Point / Solid Dot" box; move "is not equal to" and "is less than" to the "Open Dot / Bubble" box.)

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