Solve the inequality (x - 2)(x + 6) \le (x - 2)(x + 5). Write your answer in interval notation.

blackpanther Aug 12, 2024

#1**+1 **

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! :)

NotThatSmart Aug 12, 2024