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.

The required absolute inequality is |x - 78| ≤ 20.

Step-by-step explanation:

Consider the provided information.

Let $x is monthly charge.

The monthly charges for a basic cable plan = $78

it is given that it could differ by as much as $20

So, the maximum charges can be $78 + $20,

And, the minimum charges can be $78 - $20,

The value of x is lies from $78 - $20 to $78 + $20

Which can be written as:

78 - 20 ≤ x and x ≤ 78 + 20

-20 ≤ x - 78 and x - 78 ≤ 20

Change the sign of inequality if multiplying both side by minus.

20 ≥ - (x - 78) and x - 78 ≤ 20

⇒ |x - 78| ≤ 20

Thus, the required absolute inequality is |x - 78| ≤ 20.