Question Video: Given a Coordinate in a Solution Set Determine the Correct Inequality Symbol Mathematics

Video Transcript

The point four, negative two is an element of the solution set of the inequality three 𝑥 plus two 𝑦 blank eight. (A) less than, (B) greater than, (C) equal to, or (D) less than or equal to.

First, let’s think about what we know about an inequality. An inequality will have one of the four symbols: less than, greater than, greater than or equal to, or less than or equal to. If the point four, negative two is an element in the solution set, then when we plug in four and negative two, we should get a true statement. We’ll plug in four for 𝑥 and negative two for 𝑦. And then we’ll have 12 minus four compared to eight, which gives us eight.

At this point, we need to think carefully. It would be really tempting to say that eight is equal to eight. However, that is not a possible answer choice since we know that we are dealing with an inequality. We could say that eight is greater than or equal to eight; that’s still an inequality. Or we could say that eight is less than or equal to eight. Because we know that four and negative two is part of the solution set, we’ll need an inequality that contains the equal to portion. And of our four choices, that would be option (D).