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

 Dec 18, 2023
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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].

 Dec 18, 2023

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