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

kelhaku Dec 18, 2023

#1**0 **

We can solve the inequality (x - 2)(x + 6) ≤ (x - 2)(x + 5) by following these steps:

Expand both sides:

(x - 2)(x + 6) ≤ (x - 2)(x + 5) x^2 + 4x - 12 ≤ x^2 + 3x - 10

Move all terms to one side:

x^2 + 4x - 12 - (x^2 + 3x - 10) ≤ 0 x + 2 ≤ 0

Solve for the root and determine the sign:

x ≤ -2

Write the solution in interval notation:

The solution is the set of all real numbers less than or equal to -2:

x ∈ (-∞, -2]

Therefore, the solution to the inequality in interval notation is (-∞, -2].

BuiIderBoi Dec 18, 2023