|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
