Question

How do you solve `–2(x – 3) ≥ 5 – (x + 3)`?

Answer 1

`x <= 4`

Explanation:

Given
`color(white)("XXX")-2(x-3) >= 5-(x+3)`

Simplifying each side independently
`color(white)("XXX")-2x+6 >= 2-x`

We could add `2x` to both sides (you can add any amount to both sides of an inequality without effecting its validity or direction)
`color(white)("XXX")6 >=2+x`

Then, if we subtract `2` from both sides
`color(white)("XXX")4 >= x`...or, if you like your variables on the left
`color(white)("XXX")x <= 4`

Answer 2

See details below

Explanation:

First expand inequation removing braquets

`-2x+6>=5-x-3`. Now, adding to both sides in order to transpose terms, we have

`6-5+3>= -x+2x` this is the same to

`4>=x`

The inequation has as solutions all numbers `x` lower than `4`, it's say `(-oo,4]`