Question

How do you solve and graph the absolute value inequality `abs(4x + 1)≤ 5`?

Answer 1

If `(4x+1)` is positive or zero (`rarr x>= -1/4`)
and
`(4x+1)<= 5`
then
`x<=1`

If `(4x+1)` is negative (`rarr x< -1/4`)
then `abs(4x+1)<= 5`
is equivalent to
`-4x -1 <= 5`
then
`x>= -3/2`

The solution graph is the vertical band `x epsilon [-3/2,+1]`