Question

What are the solutions to the inequality (x-3)(x+5) less than or equal to zero

Answer 1

The solutions to the inequality (x-3)(x+5) less than or equal to zero are x ≤ -5 and 3 ≤ x.

Step-by-step explanation:

To find the solutions to the inequality (x-3)(x+5) less than or equal to zero, we need to determine the values of x that make the expression less than or equal to zero. The expression (x-3)(x+5) represents a quadratic function. We can solve this inequality by finding the values of x that make the quadratic function equal to zero. This will give us the x-intercepts or solutions to the inequality.

1. Set the quadratic equation equal to zero: (x-3)(x+5) = 0
2. Apply the Zero Product Property: Set each factor equal to zero and solve for x.
   • x-3 = 0 ⟹ x = 3
   • x+5 = 0 ⟹ x = -5
3. These are the x-values that make the quadratic equation equal to zero. We can plot these on a number line and determine the intervals where the expression is less than or equal to zero. The solutions are x ≤ -5 and 3 ≤ x.