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) $| x | - 40 \leq 0.75 ; ( \infty , 40.75 ]$
B) $| 40 + x | \leq 0.75 ; [ 39.25,40.75 ]$
C) $| 40 - x | \leq 0.75 ; [ 39.25,40.75 ]$
D) $| x + 0.75 | \leq 40 ; [ 39.25 , \infty )$

Question

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) $| x | - 40 \leq 0.75 ; ( \infty  , 40.75 ]$
B) $| 40 + x | \leq 0.75 ; [ 39.25,40.75 ]$
C) $| 40 - x | \leq 0.75 ; [ 39.25,40.75 ]$
D) $| x + 0.75 | \leq 40 ; [ 39.25 , \infty )$

Quizplus · Accepted Answer

The correct inequality is $| x - 40 | \leq 0.75$, which means the actual weight x can be within 0.75 pounds of 40 pounds. Solving this inequality gives the interval [39.25, 40.75].

Solve the Problem ∣x∣−40≤0.75;(∞,40.75]| x | - 40 \leq 0.75 ; ( \infty , 40.75 ]∣x∣−40≤0.75;(∞,40.75]

Solve the Problem $| x | - 40 \leq 0.75 ; ( \infty , 40.75 ]$