Question

What number is a solution of the inequality x(7-x)>8

Answer 1

8 is the number to the solution

Explanation:

An inequality is a equation that uses >,< instead of using a equal sign.

Answer 2

• any of the integers {2, 3, 4, 5}
• any real number in the range (3.5-√4.25, 3.5+√4.25)

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.