Solve the inequatitly x^2-14x+45 is less than or equal to -3
1 answer:
Answer:
6 ≤ x ≤ 8
Step-by-step explanation:
It usually works well to solve quadratic (and higher-degree) polynomial inequalities by factoring. The sign of the expression will be negative when an odd number of factors have negative signs. So, first, the inequality must be rewritten to be a comparison to zero.
x^2 -14x +48 ≤ 0 . . . . . . . . add 3 to both sides
(x -6)(x -8) ≤ 0 . . . . . . . . . . factor
Both factors will be positive when x is > 8. Both factors will be negative when x < 6, so there are no solutions in either of those regions.
The solution interval is where one factor is 0 or negative:
6 ≤ x ≤ 8
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The solution interval is shown in green on the attached graph.
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