Answer:
- any of the integers {2, 3, 4, 5}
- any real number in the range (3.5-√4.25, 3.5+√4.25)
Step-by-step explanation:
The inequality can be put in vertex form.
-x^2 +7x > 8
x^2 -7x +3.5^2 < -8 +3.5^2 . . . . . multiply by -1, complete the square
(x -3.5)^2 < 4.25 . . . . show as a square
|x -3.5| < √4.25 . . . . take the square root
-√4.25 < x -3.5 < √4.25 . . . . solve as absolute value problem
3.5 -√4.25 < x < 3.5 +√4.25
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In the attached graph, the solutions are x-values between the x-intercepts of the graphed function.
