Question

How do you solve and write the following in interval notation: `5-y>=4`?

Answer 1

`(-oo,1]`

Explanation:

`"subtract 5 from both sides"`

`cancel(5)cancel(-5)-y>= 4-5`

`rArr-y>= -1`

`"multiply through by - 1"`

`color(blue)"NOTE"` when multiplying/dividing by a negative quantity `color(red)"Reverse"` the inequality symbol.

`rArry<= 1larrcolor(red)" reverse symbol"`

`"in interval notation " (-oo,1]`

Answer 2

Solution: `y<=1`. In interval notation : `(-oo,1]`

Explanation:

`5-y >= 4 or -y >= 4-5 or -y >= -1 or y <= 1`

Note: multiplying with negative on both sides will reverse the inequality sign.

Solution: `y<=1`. In interval notation : `(-oo,1]` [Ans]