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| ≥ 20
B.) |x − 20| ≥ 78
C) |x − 20| ≤ 78
B.) |x − 78| ≤ 20

D) |x − 78| ≤ 20

Step-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| ≤ 20

Which is the required absolute value inequality to determine the range of basic cable plan costs,

Option 'D' is correct.

maybe i can

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1