Question

Needed help to catch up before summer come any help will be good thank you

Answer 1

We have the following set of inequations

`\begin{cases}y-2<-5{} \\ y-2>{5}\end{cases}`

Let's solve both for y, it will give us

`\begin{cases}y<-5{+2} \\ y>{5}+2\end{cases}\Rightarrow\begin{cases}y<-3 \\ y>7\end{cases}`

Therefore y must be smaller than -3 and bigger than 7, then, the set between -3 and 7 is not part of the solution. the solution in fact is

`S=(-\infty,-3)\cup(7,+\infty)`

Let's do it in the graph!

The solution to the inequations is in blue on the graph.