Question

Solve each compound Inequality.

42. -2 ≤ d + 1/2 < 4 1/2
44. 2t ≤ -4 or 7t ≥ 49
46. -1 ≤ a - 3 ≤ 2
48. A town's high temperature for a given month is 88 degrees Fahrenheit and the low temperature is 65 degrees Fahrenheit. Write a compound inequality to represent the range of temperatures for the given month.

Answer 1

42.
-2 ≤ d + 1/2 < 4 1/2 (-1/2)
-2 1/2 ≤ d ≤ 4

44.
2t ≤ -4 or 7t ≥ 49
2t ≤ -4 (/2)
t ≤ -2
7t ≥ 49 (/7)
t ≥ 7

46.
-1 ≤ a - 3 ≤ 2 (+3)
2 ≤ a ≤ 5

The key to solving these types of questions is to think to yourself - what do I need to do to get the variable on its own? Then, apply this action to every part of the inequality separated by inequality signs. When you get two separate inequalities describing the value of the variable, just think about them separately and apply the same logic.

All you have to do for the last question (48.) is turn the question into an inequality. Calling the temperature t:

65 ≤ t ≤ 88

Notice the use of greater-than-or-equal symbols - this is because 65 and 88 were recorded temperatures, so are included in the range of values for t

I hope this helps