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Solve: x+2/x-4<0

A –4 < x < –2
B –2 < x < 4
C –2 < x < –4
D –4 < x < 2

1 Answer

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Answer:

B. -2 < x < 4

Explanation:

The function is (x +2)/(x-4) and we are asked to determine the x interval when the inequality (x +2)/(x-4) < 0 is satisfied

1. Find the critical points

The critical points are

x = - 2 when the numerator becomes -2 + 2 = 0, and f(x) = 0

and

x = 4 when the denominator becomes 4 - 4 = 0 and (x + 2)/0 is undefined

So critical points are -2 and 4

2. Use these critical points to divide the number line into intervals
The intervals are -∞ < x < -2, -2 < x < 4 and 4 < x < ∞
these can be re-written as x < -2, -2 < x < -4 and x > 4

3. For each of these intervals take a test point and see if it satisfies that inequality
(a) -∞ < x < -2 Take x = -3 which is less than -2
We get f(-3) = (-3 + 2)/(-3 -4) = -1/-7 which is + 1/7 and does not satisfy the (x+2)/(x-4) < 0 inequality.

So we can discard this interval
(b) For interval -2 < x < 4, Let's take x = 0
(0+2)/(0-4) = 2/(-4) = -1/2 = -0.5 which does satisfy the inequality
(x+2)/(x-4) <0, so this is a valid interval

(c) For interval x > 4, take x = 5
(x+2)/(x-4 ) = (5 + 2)/(5-4) = 7/1 = 7 and does not satisfy (x+2)/(x-4 ) < 0

So the interval which satisfies the inequality is -2 < x < 4

Solve: x+2/x-4<0 A –4 < x < –2 B –2 < x < 4 C –2 < x < –4 D –4 &lt-example-1
User Sterlin
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