Question

Which of the following represents the solution to the inequality 215-2xl-3315?

O (-60,-2) (7.00)
O (-0,1.5) (7.5.00)
O 1-2, 7]
O [1.5, 7.5]

Answer 1

9514 1404 393

Answer:

(c) [-2, 7]

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.