Which inequality has solution set (-∞, ∞)?
A. (x-3)^2≥0 B. (5x-6...

Question

Which inequality has solution set (-∞, ∞)? 
A. (x-3)^2≥0 B. (5x-6)^2≤0 C. (6x+4)^2>0 D. (8x+7)^2<0

Accepted Answer

Hello everyone. In this video, we're going to be looking at this practice problem where we want to determine which of the inequalities will fit the solution set of being all real numbers, which is negative infinity to positive infinity. That means that we can plug in all numbers into X and we get a valid answer or the inequality is true. So in this case, whenever we square a number, that number will always be, or whenever we raise A number to the 10th power, it will only be greater than or equal to zero where an is even. So in this case, you can see that all of the inequalities are raised to the even power of two. So they will all be greater than or equal to zero because they're being squared. So negative times negative will always be a positive. So if we look at the answer choices, you can see that answer choice A is the only one that is saying that the component that is being squared will be greater than or equal to zero. While the other ones are saying that Be saying that the component will be less than or equal to 0D is also saying that and C is saying greater than, but not equal to. And in this case, if we plug in Seven into this first one, we have 7 -7 squared is greater than or equal to zero. And as you can see, it says zero is greater than or equal to zero. So that is true. And similarly, we can disprove this greater than or equal to By plugging in x equals negative 8.5. So if I do two times negative 8. Plus 17, this becomes negative 17 plus squared, we still have the squared. So it's become zero squared. And now you can see that this inequality where it says zero is greater than zero is not true. So answer choice A ends up being the only inequality where the solution set negative infinity to positive infinity infinity would be true because it follows this form where the component that's being squared is greater than or equal to zero. So hopefully this video helped and see you next time.

Which inequality has solution set (-∞, ∞)? A. (x-3)^2≥0 B. (5x-6)^2≤0 C. (6x+4)^2>0 D. (8x+7)^2<0

Key Concepts

Inequalities

Quadratic Expressions

Solution Sets

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