Solve this Inequality! One of the examples to solve in the book is:
$$ 
-3<4-x<2 \quad\text{and}\quad -1 \leq x-5 \leq 2
$$
What I've done so far:
I've solved each inequality getting to $7>x>2$ and $4 \leq x \leq 7$
All I need to do now is to make it into one equality, I can do it when there is only 2 parts to the inequality but not when there is 3
Thanks!!
 A: Once you get the two separate inequalities
$$
\begin{cases}
\color{red}{2 < x < 7} \\[5pt]
\color{blue}{4 \leq x \leq 7}
\end{cases}
$$
it is convenient to represent them graphically. Just represent the real numbers as a straight line and mark the numbers that appear in you inequalities in the correct order from the lowest to the highest (their position need not be properly scaled though) as in the picture ($2$, $4$ and $7$ in your case).

Then represent each inequality as a rectangle as shown in the picture. Different inequalities should correspond to rectangles of different heights. It is convenient to (for instance) mark the top corners with either filled or hollow circles: filled circles tell you that the inequality includes the corresponding point, while hollow circles tell you they do not. In your example


*

*in the equation $\color{red}{2<x<7}$, since neither $2$ and $7$ are part of the solution, then you mark both the top vertices with a hollow circle;

*in the equation $\color{blue}{4\leq x\leq 7}$, both $4$ and $7$ are part of the solution, therefore the corresponding vertices are to be marked with a filled circle.


Since you are looking for the intersection of the two equations, you are interested in the region (of the real line) that belongs to both the two, i.e. the one that goes from $4$ to $7$.
Now, how can we tell whether $4$ and $7$ are part of the solution or not? That's where hollow and filled circles help us out: it should be easy to understand that the solution turns out to be
$$
 4 ~\leq~ x ~<~ 7
$$
Can you tell why?
(edit) Further details:
Consider the following system of inequalities:
$$
\begin{cases}\tag{S}
\color{red}{2 < x < 7 \quad\vee\quad 9\leq x<11} \\[5pt]
\color{blue}{4 \leq x < 10}
\end{cases}
$$
The '$\vee$' sign (logical or, set union) can be graphically translated as "draw another rectangle of the same height". Therefore the system (S) corresponds to the following graphical representation:

The solution, again, is the area spanned by both $\color{red}{red}$ and $\color{blue}{blue}$ rectangles, that is
$$
4 \leq x < 7 \quad\vee\quad 9\leq x <10
$$
It should be straightforward to understand how all these reasonings apply to systems of more than two inequalities as well.
A: You did first part right
$7>x>2$
$(2)$
$-1 \le x-5\le2$
$4 \le x\le7$
combining both parts we ,get
$4 \le x<7$ (you can check it ,by representing in number line)
Represent  solution of both parts in number line
Your new solution is intersection of both parts 
