Question

exnc. 71–72: solve part (a) and use the answers to parts (b) and (c)
71 (a) |x + 5| = 3
(b) |x + 5| < 3
(c) |x + 5| > 3
72 (a) |x - 3| < 2
(b) |x - 3| = 2
(c) |x - 3| > 2
exnc. 73–76: express the statement in terms of an inequality by involving an absolute value.
73 the weight w of a wrestler must be within 2 pounds of 148 pounds.
74 the radius r of a ball bearing must be within 0.01 centimeter of 1 centimeter.
75 the difference of two temperatures t₁ and t₂ within a chemical mixture must be between 5°c and 10°c.
76 the arrival time t of train b must be at least 5 minutes different from the 4:00 p.m. arrival time of train a.
77 temperature scales temperature readings on the fahrenheit and celsius scales are related by the formula c = \\(\frac{5}{9}\\)(f - 32). what values of f correspond to the values of c such that 30 ≤ c ≤ 40?

Explanation:

Problem 73:

Step1: Understand the absolute value inequality for "within 2 pounds of 148 pounds"

The weight \( w \) is within 2 pounds of 148, so the difference between \( w \) and 148 is less than or equal to 2. In absolute value terms, this is \( |w - 148| \leq 2 \).

Step1: Translate "within 0.01 centimeter of 1 centimeter" to absolute value

The radius \( r \) is within 0.01 of 1, so \( |r - 1| \leq 0.01 \).

Step1: Analyze the temperature difference range

The difference \( |T_1 - T_2| \) must be between 5 and 10, so \( 5 \leq |T_1 - T_2| \leq 10 \).

Answer:

\( |w - 148| \leq 2 \)

Problem 74: