Solve the inequality:
(x + 2)(x - 7) ≥ 0
The product of x + 2 and x - 7 can only be 0 if any (or both) of the factors is 0.
The product can only be positive if both are positive or both are negative. These conditions can be expressed as:
x + 2 ≥ 0 and x - 7 ≥ 0
OR
x + 2 ≤ 0 and x - 7 ≤ 0
The first pair of conditions lead to:
x ≥ -2 and x ≥ 7
The combination of both conditions produces a single solution:
x ≥ 7
The second pair of conditions lead to:
x ≤ -2 and x ≤ 7
The combination of both conditions produces a single solution:
x ≤ -2
The total solution to the inequality is:
x ≤ -2 U x ≥ 7
U = Union
The graph of the solution is: