Solve the inequatitly x^2-14x+45 is less than or equal to -3

  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.

step-by-step explanation:

the shape,the size and the distance