# need help trying to figure out what the teacher is asking me to explain

Anonymous

Question description

You have the right ideas but more explanation is required.

x − 3/ x + 2 ≤ 0 Should be (x − 3)/(x + 2) ≤ 0 The parentheses matter when the expression is typed on a single line

(x−3)=0

(x+2)=0

x = 3

x = -2

≤ -2

-2 ≤ ≤ 3

3 ≤ x

x ≤ -2

-2 ≤ ≤3    3 ≤ x

-2 ≤ ≤ 3

-2 < ≤ 3  <--- How do you know that this is the final answer?

(−2,3] Correct

You are correct to initially consider three intervals.

< -2

-2 < < 3

3 < x

To figure out which interval(s) belong in the solution set, you can explain via a test value approach.

For each interval, pick a test value and see if it satisfies the (x − 3)/(x + 2) ≤ 0 inequality. If so, then the interval is in the solution set.

For instance, for < -2 we could pick -5 as a test value.

(-5 − 3)/(-5 + 2) = (-8)/(-3) = 8/3 is not < 0, so < -2 is not in the solution set.

Please show the test value approach for all three intervals.

Then consider whether the endpoints should be included. How do you know that 3 is included but -2 is not? Please explain a bit.

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