Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. \[ (x-7)(x+9)>0 \] Use the inequality in the form $f(x)>0$, to write the intervals determined by the boundary points as they appear from left to right on a number line. (Type your answers in interval notation. Use ascending order.)

Step 1 ：The inequality is a product of two factors, (x-7) and (x+9), and we are looking for the values of x for which this product is greater than 0. The product will be greater than 0 when both factors are positive or both are negative.

Step 2 ：The factors are zero at x=7 and x=-9. These are the boundary points that divide the number line into three intervals: (-∞, -9), (-9, 7), and (7, ∞).

Step 3 ：We need to test a number from each interval in the inequality to determine where the inequality holds. For the interval (-∞, -9), we can test x=-10. For the interval (-9, 7), we can test x=0. For the interval (7, ∞), we can test x=10.

Step 4 ：We will substitute these test points into the inequality and see if the inequality holds. If it does, then the interval is part of the solution set.

Step 5 ：The test points x=-10 and x=10 satisfy the inequality, which means the intervals (-∞, -9) and (7, ∞) are part of the solution set. The test point x=0 does not satisfy the inequality, so the interval (-9, 7) is not part of the solution set.

Step 6 ：\(\boxed{\text{The solution set of the inequality is } (-∞, -9) \cup (7, ∞)}\)