Question

How do you solve `4 > 3x + 3 or 9 ≤ - 5x + 3`?

Answer 1

Solve compound inequalities.

Explanation:

(1) 4 > 3x + 3 --> 3x < 4 - 3 --> `x < 1/3`

(2) `9 <= - 5x + 3 -> - 5x >= 6` --> `x <= -6/5`

Answer 2

`x<1/3`

Explanation:

Part 1: `4>3x+3`
`4>3x+3`
`color(white)("XXXX")`subtract 3 from both sides
`1>3x`
`color(white)("XXXX")`divide both sides by 3
`1/3>x`

Part 2: `9<=−5x+3`
`9<=-5x+3`
`color(white)("XXXX")`subtract 3 from both sides
`6<=-5x`
`color(white)("XXXX")`divide both sides by `(-5)` remembering to reverse the inequality orientation because of the negative division.
`-6/5>=x`

Part 3: combining with or
If it is only necessary for
`color(white)("XXXX")` `x<1/3`
or
`color(white)("XXXX")` `x<=-6/5`
then
it is only necessary for
`color(white)("XXXX")` `x<1/3`
`color(white)("XXXX")` `color(white)("XXXX")`since `(x<=-6/5)` is a subset of `(x<1/3)`)