A cable company claims that the average household pays $78 a month for a basic cable plan, but it could differ by as much as $20. Write an absolute value inequality to determine the range of basic cable plan costs with this cable company.A. |x − 78| ≥ 20B. |x − 20| ≥ 78C. |x − 20| ≤ 78D. |x − 78| ≤ 20

Answer:D) |x − 78| ≤ 20Step-by-step explanation:Given,The monthly charges for a basic cable plan = $ 78,Also,  it could differ by as much as $20,So, the maximum charges = $(78 + 20) ,And, the minimum charges = $(78 - 20),Let x represents the monthly charges ( in dollars ),78 - 20 ≤ x ≤ 78 + 20⇒ 78 - 20 ≤ x and x ≤ 78 + 20⇒ -20 ≤ x -78 and x-78 ≤ 20⇒ 20 ≥ -(x-78) and x-78 ≤ 20   ( ∵ a > b ⇒ -a < -b )⇒ |x-78| ≤ 20Which is the required absolute value inequality to determine the range of basic cable plan costs,Option 'D' is correct.