Question

How do you graph the inequality `6(y+1)< -x`?

Answer 1

Supporting Brian's solution

Just another way of showing the inequality and a tip about method.

Explanation:

`color(brown)("You can manipulate an inequality the same way you do an equation.")` Just be mindful of this (by example and using numbers to make my point), suppose we had
`-3< 4`

If we multiply by `(-1)` but do not change the inequality we have

`+3<-4 color(red)(" This is false!")`

Be mindful of what the inequality is doing.

We should have had: `(-1)(-3<4) -> color(green)(3 > -4 )`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Solving your question")`

Given:

`6y+6<-x`

Subtract 6 from both sides

`6y<-x-6`

Divide both sides by 6

`6/6 y<-x/6-1`

But `6/6=1`

`y<-x/6-1`