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:
[tex]|x|= \left \{ {{x,{ifx\ \textgreater \ 0} \atop {-x},ifx\ \textless \ 0} \right. [/tex]
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.
