Question

Match the compound inequalities below with one of the statements in the table. Not all inequalities will be used.

-42 < x < 102: All real numbers between -42 and 102, inclusive.
0 < x < 6: All real numbers that are less than six but more than 0.
x ≤ 10: All positive real numbers less than or equal to ten.
x > 85 or x < 65: All students earning above an 85 or below a 65 were asked to report to the media center for further instructions.
20 ≤ x < 32: The expected weight must be greater than or equal to 20 pounds but less than 32 pounds.
x < 25 or x >= 62: Students under 25 or seniors at or above 62 get a discount.
x ≥ 72 or x < 54: If the temperature is at or above 72℉ or below 54℉, the samples in the biology lab are no longer useful.
16 ≤ x < 20: Cookies must be baked between 16 and 20 minutes.

Answer 1

The compound inequalities are matched with their respective real-world scenarios, such as 0 < x < 6 matching with quantities less than six but more than zero, and x ≥ 72 or x < 54 matching with temperatures that make biology samples useless.

Step-by-step explanation:

To match the compound inequalities with the corresponding real-world scenario:

• -42 < x < 102: This does not match with any given statements as there is no inclusive statement for these endpoints.
• 0 < x < 6 corresponds to the statement 'All real numbers that are less than six but more than 0'.
• x ≤ 10: This inequality represents 'All positive real numbers less than or equal to ten'.
• x > 85 or x < 65 aligns with 'All students earning above an 85 or below a 65 were asked to report to the media center for further instructions'.
• 20 ≤ x < 32 relates to 'The expected weight must be greater than or equal to 20 pounds but less than 32 pounds'.
• x < 25 or x >= 62 corresponds to 'Students under 25 or seniors at or above 62 get a discount'.
• x ≥ 72 or x < 54 aligns with the scenario 'If the temperature is at or above 72℉ or below 54℉, the samples in the biology lab are no longer useful'.
• 16 ≤ x < 20 matches with 'Cookies must be baked between 16 and 20 minutes.'