Select the graph that would represent the best presentation of the solution set. |1 - 4x| > 7

Hi, the set of graph choices is missing. Nevertheless, I can solve the inequality, find the soluction set and graph it.

Remember the definition of the absolute value function:



So, to solve |1-4x|>7, you have to considerer two cases:

1) Case 1: If 1 - 4x > 0, the solution is:

1 - 4x > 7

Which you solve in this way:

subtract 1 in both sides ⇒         -4x > 6
divide by - 4 ⇒                             x < -6/4
simplify the fraction                      x < -3/2

2) Case 2: If 1 - 4x < 0, the solution is:

1 - 4x < - 7 ⇒

subtract  -1:                                - 4x < - 8
divide by - 4:                                   x > 8/4
simplify the fraction:                       x > 2

Therefore the solution is (-∞, -3/2) ∪ (2,∞), whose graph is the one attached.

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.