|2-x|≤3  To remove absolute value bars write this:

 -3 < 2-x < 3   Solve for x in the middle:

Clear of fractions by multiplying through by 7

Get rid of the 42 in the middle by adding -42 to all three sides:

-21 ≤ 42-7x ≤  21
-42  -42      -42
-63 ≤   -7x ≤ -21

We must divide through by -7, but when we divide through
by a negative number we must reverse the inequalities:

 ≥  ≥ 

9 ≥ x ≥ 3

This is equivalent to

3 ≤ x ≤ 9  it is usually preferred to write it with ≤ rather than ≥:

The solution is   3 ≤ x ≤ 9

The graph of the solution set is this:

--------⚫====================⚫---------  
        3                    9  

Since we have ≤ and not < we include the endpoints of the interval,
and use darkened circles at the endpoints to indicate this.

The interval notation for the solution set is this:

            [3,9]

and we use brackets [ ] instead of parentheses ( ) to indicate that
the endpoints are both included in the solution set.

Edwin