9514 1404 393
Answer:
(c) [-2, 7]
Step-by-step explanation:
We can solve the inequality for an expression in x.
2|5 -2x| -3 ≤ 15
2|5 -2x| ≤ 18 . . . . . . add 3
|5 -2x| ≤ 9 . . . . . . . . divide by 2
We prefer a positive coefficient of x, so we'll multiply inside the absolute value by -1. This does not change the absolute value. (|-1| = |1|, for example)
|2x -5| ≤ 9
Now, we can "unfold" this to get the compound inequality ...
-9 ≤ 2x -5 ≤ 9
-4 ≤ 2x ≤ 14 . . . . . add 5
-2 ≤ x ≤ 7 . . . . . . . divide by 2
The solution interval is [-2, 7].
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The graph shows the equation of the given form f(x) ≤ c converted to the form f(x)-c ≤ 0. The graphing calculator highlights x-intercepts easily, so we take advantage of that to show the solution interval bounds. The graph is less than zero between the bounds.
