Explanation:
The product of two factors is positive if both factors have the same sign (both positive or both negative). So, we need to determine the intervals on the number line where the expression 5(x - 3)(x+3) is positive.
We can use a sign chart to determine the sign of the expression in each interval:
| interval | x - 3 | x + 3 | (x - 3)(x + 3) |
|--------------|---------|---------|-----------------|
| x < -3 | negative | negative | positive |
| -3 < x < 3 | negative | positive | negative |
| x > 3 | positive | positive | positive |
The expression is positive in the intervals where (x - 3)(x + 3) is positive, which are the intervals x < -3 and x > 3. Therefore, the solution to the inequality is:
x < -3 or x > 3
This means that x can be any value less than -3 or any value greater than 3. To express the solution set in interval notation, we can write:
(-∞, -3) U (3, ∞)
Therefore, the solution to the inequality 5(x - 3)(x+3) > 0 is (-∞, -3) U (3, ∞).