Question

How to solve (x+7)(x-9)>0

Answer 1

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Answer:

  (x < -7) ∪ (x > 9)

Step-by-step explanation:

The zeros of the function are the values of x that make the factors zero.

  x +7 = 0   ⇒   x = -7

  x -9 = 0   ⇒   x = 9

When this is expanded, we can see that the leading coefficient is positive.

  x² -2x -63 > 0

This means the parabola opens upward. It will be greater than 0 for x-values to the left of the left zero, and to the right of the right zero. (It is less than zero between those values.)

The solution is x < -7 or x > 9.

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In general, for polynomial inequalities, look for the locations of the zeros. The sign of the polynomial will have the sign of the leading coefficient for values of x to the right of the right-most zero. (Here, positive for x > 9.) As you progress farther to the left along the number line, the polynomial changes sign at each zero.

Here, the polynomial becomes negative between the values x=9 and x=-7. Then it is positive again for x < -7.