Solve the inequality (x - 2)(x + 6) \le (x - 2)(x + 5). Write your answer in interval notation.
We don't have the expand everything, as we can just use factoring to our advantage.
Moving all terms to the right side of the equation, we get
\( (x - 2)(x + 6) - (x - 2)(x + 5) \leq 0\)
Now, since both terms have x- 2, we can factor it out to get
\((x-2)(x+6 - (x+5)) \le 0\\ (x-2)(x+6-x-5) \leq 0 \\ x-2 \leq 0\)
Isolating x from the equation, we get
\(x \le 2\)
In interval notation, this is \((-\infty, 2]\)
Thanks! :)