Question

(x+6)(x+2)<0 помогите пожалуйста

Answer 1

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Answer 2

Solving the Inequality (x+6)(x+2) < 0

To solve the inequality (x+6)(x+2) < 0, we can use the method of intervals and the concept of sign analysis.

First, let's find the critical points by setting each factor equal to zero and solving for x: 1. (x+6) = 0 => x = -6 2. (x+2) = 0 => x = -2

Now, we can use these critical points to divide the number line into intervals and determine the sign of the expression (x+6)(x+2) in each interval.

- When x < -6, both (x+6) and (x+2) are negative, so their product is positive. - When -6 < x < -2, (x+6) is positive and (x+2) is negative, so their product is negative. - When x > -2, both (x+6) and (x+2) are positive, so their product is positive.

Now, we can determine the solution to the inequality based on the sign analysis.

Solution: The solution to the inequality (x+6)(x+2) < 0 is the interval where the expression is negative, which is -6 < x < -2.

Therefore, the solution to the inequality is -6 < x < -2.

This means that the inequality is satisfied when x is between -6 and -2, exclusive of the endpoints.

I hope this helps! If you have any further questions, feel free to ask.