Solve the problem.
-A landscaping company sells 40 -pound bags of top soil. The actual weight $x$ of a bag, however, may differ from the advertised weight by as much as $0.75$ pound. Write an inequality involving absolute value that expresses the relationship between the actual weight $x$ of a bag and 40 pounds. Solve the inequality, and express the answer in interval form.
A) $| 40 - \mathrm { x } | \leq 0.75 ; [ 39.25,40.75 ]$
B) $| 40 + x | \leq 0.75 ; [ 39.25,40.75 ]$
C) $| x + 0.75 | \leq 40 ; [ 39.25 , \infty )$
D) $| x | - 40 \leq 0.75 ; ( - \infty , 40.75 ]$

Question

Quizplus · Accepted Answer

The absolute value inequality that expresses the relationship between the actual weight x and 40 pounds is |40 - x| ≤ 0.75. This is because the actual weight x can be as much as 0.75 pound more or less than the advertised weight of 40 pounds. Simplifying this inequality, we get -0.75 ≤ 40 - x ≤ 0.75, which can be written as 39.25 ≤ x ≤ 40.75. Therefore, the answer is A, with the interval [39.25, 40.75].

Solve the Problem xxx Of a Bag, However, May Differ from the Advertised Weight

Solve the Problem $x$ Of a Bag, However, May Differ from the Advertised Weight