Question

How do you solve `3- 8x \geq - 4x + 3`?

Answer 1

we get `x<=0`

Explanation:

Adding `8x`
we get
`3>=4x+3`
after subtracting `3`
we get

`0>=4x`
or
`0>=x`

Answer 2

`x <= 0`

Explanation:

`3 - 8x >= -4x + 3`

First, add `color(blue)(4x)` to both sides of the inequality:
`3 - 8x quadcolor(blue)(+quad4x) >= -4x + 3 quadcolor(blue)(+quad4x)`

`3 - 4x >= 3`

Subtract `color(blue)3` from both sides:
`3 - 4x quadcolor(blue)(-quad3) >= 3 quadcolor(blue)(-quad3)`

`-4x >= 0`

Now we need to divide `color(blue)(-4)` on both sides, but every time we divide by a negative sign, we have to flip the inequality. So the inequality becomes a `<=` instead of a `>=`:
`(-4x)/color(blue)(-4) >= 0/color(blue)(-4)`

Therefore,
`x <= 0`

Hope this helps!