Convert to Interval Notation x^2+x>6

Problem

x2+x>6

Solution

1. Rearrange the inequality to one side so that it is compared to zero by subtracting 6 from both sides.

x2+x−6>0

2. Factor the quadratic expression on the left side to find the critical points.

(x+3)*(x−2)>0

3. Identify the critical points by setting each factor equal to zero, which gives x=−3 and x=2

4. Test the intervals created by the critical points: (−∞,−3) (−3,2) and (2,∞)

• For x=−4 (−4+3)*(−4−2)=(−1)*(−6)=6 which is >0

• For x=0 (0+3)*(0−2)=(3)*(−2)=−6 which is not >0

• For x=3 (3+3)*(3−2)=(6)*(1)=6 which is >0

5. Select the intervals where the expression is positive, as indicated by the "greater than" sign.

Final Answer

x2+x>6⇒(−∞,−3)∪(2,∞)

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