Convert to Interval Notation x^2<10-3x

Problem

x2<10−3*x

Solution

1. Rearrange the inequality into standard quadratic form by moving all terms to one side.

x2+3*x−10<0

2. Factor the quadratic expression to find the critical points where the expression equals zero.

(x+5)*(x−2)<0

3. Identify the critical points by setting each factor to zero.

x=−5

x=2

4. Test the intervals created by the critical points: (−∞,−5) (−5,2) and (2,∞)
   For x=0 in the interval (−5,2)

(0)2+3*(0)−10=−10

Since −10<0 the inequality holds true for this interval.

5. Determine the solution set based on the inequality sign. Since the inequality is strictly less than (<, use parentheses to indicate that the endpoints are not included.

(−5,2)

Final Answer

x2<10−3*x⇒(−5,2)

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