NECT IT Use the problem from the previous page to help you understand how to write and graph one-variable inequalities. (1) Look at the first Model It. The inequality for the Standard tour uses a symbol that combines the less than symbol $$ (

Question

NECT IT
Use the problem from the previous page to help you understand how to write and graph one-variable inequalities.
(1) Look at the first Model It. The inequality for the Standard tour uses a symbol that combines the less than symbol with the equal sign . Why do you need to use equal to, as well as less than, when describing all possible values for s?
(2) Why does the inequality for the Advanced tour use only the less than symbol?

3 Look at the second Model It. Why does one graph have a closed circle at the en of the arrow, while the other graph has an open circle?
(4) Raúl uses a greater than or equal to to write the inequality . Does this inequality also represent the graph for the Standard tour? Explain

Ask by Maxwell Bright. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

1. The Standard tour’s inequality uses the symbol $$ \leq $$ (which combines “less than” and “equal to”) because the endpoint value is included in the roster of acceptable values for $$ s $$. In other words, if $$ s $$ is exactly equal to that boundary number, it still qualifies as part of the tour. Without the “equal to,” the endpoint would be excluded.

2. The inequality for the Advanced tour uses only the $$ < $$ symbol because the endpoint value is not included. This means that while $$ s $$ must be less than the boundary, it cannot equal the boundary value, which is why the “equal to” portion is omitted.

3. In the graphs, a closed circle indicates that the endpoint is included in the solution set (as with the inequality that uses $$ \leq $$ or $$ \geq $$), whereas an open circle means the endpoint is not part of the solution (as with strict inequalities using $$ < $$ or $$ > $$). Hence, one graph has a closed circle at the end of the arrow to show inclusion of the endpoint, while the other graph has an open circle to show that the endpoint is excluded.

4. Raúl’s inequality $$ 16 \geq s $$ is equivalent to $$ s \leq 16 $$. Since the Standard tour’s inequality is defined to include the endpoint (using “equal to”), Raúl’s inequality does indeed represent the same graph as that for the Standard tour. The form simply reverses the sides of the inequality, but the relationship between $$ s $$ and 16 remains unchanged.
1. The Standard tour uses $$ \leq $$ to include the exact boundary value for $$ s $$, ensuring it's part of the solution. 2. The Advanced tour uses $$ < $$ to exclude the boundary value, meaning $$ s $$ must be strictly less than the boundary. 3. A closed circle on a graph shows the endpoint is included, while an open circle shows it's excluded. 4. Raúl’s $$ 16 \geq s $$ is the same as $$ s \leq 16 $$, so it matches the Standard tour’s graph.

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