Question

How do you solve and graph `5-(x+4)<= -3`?

Answer 1

`x >= 4`

Explanation:

`5-(x+4) <= -3`

Distribute the negative sign on the left side:
`5 - x - 4 <= -3`

Simplify:
`1 - x <= -3`

Add `color(blue)(x)` to both sides:
`1 - x quadcolor(blue)(+quadx) <= -3 quadcolor(blue)(+quadx)`

`1 <= -3 + x`

Add `color(blue)(3)` to both sides:
`1 quadcolor(blue)(+quad3) <= -3 + x quadcolor(blue)(+quad3)`

`4 <= x`

Therefore,
`x >= 4`

Here's a graph of it on a number line:

(mathwarehouse.com)

The closed circle on `4` means that it is a solution (and anything greater than it is).

Hope this helps!