Final answer:
To find the solution set to the inequality 5(x - 2)(x + 4) > 0, set each factor equal to zero, draw a number line, choose test values, determine the sign of the expression, and write the solution set.
Step-by-step explanation:
The solution set to the inequality 5(x - 2)(x + 4) > 0 can be found by considering the sign of each factor and identifying the intervals where the inequality is true. Here's the step-by-step process:
- Set each factor equal to zero: (x - 2) = 0 and (x + 4) = 0. Solve for x to find the critical values: x = 2 and x = -4.
- Draw a number line and mark the critical values.
- Choose test values in each interval (e.g., x = -5, x = 0, x = 3) and determine the sign of the expression 5(x - 2)(x + 4).
- Based on the signs of the expression, determine the intervals where the inequality is true. For example, if the expression is positive in an interval, then that interval is part of the solution set.
- Write the solution set using interval notation, indicating whether the inequality is strict (>) or non-strict (≥).
The solution set for the inequality is (-∞, -4) ∪ (-4, 2) ∪ (2, +∞).