Question

How do you solve the inequality `-4z-7<9`?

Answer 1

`z > -4`

Explanation:

`-4z - 7 < 9`

Add `color(blue)(4z)` to both sides:
`-4z - 7 quadcolor(blue)(+quad4z) < 9 quadcolor(blue)(+quad4z)`

`-7 < 9 + 4z`

Subtract `color(blue)9` from both sides:
`-7 quadcolor(blue)(-quad9) < 9 + 4z quadcolor(blue)(-quad9)`

`-16 < 4z`

Divide both sides by `color(blue)4`:
`(-16)/color(blue)4 < (4z)/color(blue)4`

`-4 < z`

Therefore,
`z > -4`

Hope this helps!

Answer 2

`z> -4`

Explanation:

Our end goal is to isolate `z`, so let's start by adding `7` to both sides. We're left with

`-4z<16`

Next, to isolate `z` further, let's divide both sides by `-4`. Recall that when we apply a negative to an inequality, the sign flips.

We now have

`z> -4`

Hope this helps!