Question

How do you solve -4x-1>3 or x+2>7?

Answer 1

`x < -1 or x > 5`
`color(white)("XXX")`OR
`abs(x-2) > 3`

Explanation:

Part 1
`color(white)("XXX")-4x-1 > 3`
add `4x-3` to both sides
`color(white)("XXX")-4 > 4x`
divide by `4`
`color(white)("XXX")-1 > x`
or, equivalently
`color(white)("XXX")x < -1`

Part 2
`color(white)("XXX")x+2 > 7`
subtract `2` from both sides
`color(white)("XXX")x > 5`

Note that for `x < -1` or `x > 5`
`color(white)("XXX")x` must be further that `2` the midpoint between `(-1)` and `(5)` (i.e. from `3`)
So
`color(white)("XXX")abs(x-2) > 3`