Solve the inequality and give your answer in interval notation. Make sure to show your complete sign chart analysis including factors, test intervals, test values, and results.

Question

Solve the inequality and give your answer in interval notation. Make sure to show your complete sign chart analysis including factors, test intervals, test values, and results.

3x^2+22x≤16

Please help solve it!

Answer 1

First we should try to factor the given inequality:

3x² + 22x <= 16

3x² + 22x - 16 <= 0

(3x - 2)(x + 8) <= 0

Based on this factoring, we know there are two zeros, at x = -8 and x = 2/3. So there are three intervals we are interested in:

(-∞, -8], [-8, 2/3], and [2/3, ∞).

I'll leave it up to you to test these three intervals and determine which one(s) are the correct ones!