Question

How do you solve `-2x + 3\geq 4x - 9`?

Answer 1

`x <= 2`

Explanation:

`-2x + 3\geq 4x - 9`

Treat this is the same way as an equation unless you multiply or divide by a negative number in which case the sign in the middle changes around.
However, it is always possible to avoid having to do that if you keep the variable positive.

`cancel(-2x) + 3 cancel(+2x) \geq 4x - 9+2x" "larr` add `2x` to both sides

`3 >= 6x -9" "larr` add 9 to both sides

`3+9 >= 6x-9+9`

`12 >= 6x" "larr div 6`

`2 >= x`

This can also be written as `x <= 2`