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

**Question description**

Teacher's comments:

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

*x *≤ -2

-2 ≤ *x *≤ 3

3 ≤ *x*

* x *≤ -2

-2 ≤ *x *≤3 3 ≤ *x*

-2 ≤ *x *≤ 3

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

(−2,3] **Correct**

**You are correct to initially consider three intervals.**

*x *< -2

-2 < *x *< 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 x < -2 we could pick -5 as a test value.**

**(-5 − 3)/(-5 + 2) = (-8)/(-3) = 8/3 is not < 0, so x < -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.**

**Please reply to address the comments. Thanks!**

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