Question

solve
| 1 - 4x | >7

Answer 1

-7>1-4x>7

Answer 2

aaaaaaaaaaaaagh. there is no such thing as
\[-7>1-4x>7\]

Answer 3

your answer will be two intervals, since you have an absolute value greater than some number, so you have to solve two separate inequalities and get two separate intervals

Answer 4

\[-7> blah>7\] means you think there is something that is simultaneously less that -7 and at the same time greater than 7, and i assure you there is not

Answer 5

\[1-4x>7\]
\[1-4x<-7\]

Answer 6

what ileden said

Answer 7

yes , the answer will be union of two intervals.
This is just a combined representation of two inequalities which makes solving easier and faster.

Answer 8

and if you prefer not to mess with
\[1-4x\] because of the annoying negative coefficient you can also write as a first step
\[|4x-1|>7\] and solve
\[4x-1>7\] or
\[4x-1<-7\] your choice

but i assure you you cannot solve
\[-7>1-4x>7\] however tasty you might think it is

Answer 9

caveat emptor