Video Transcript
Which of the relation symbols below makes the following statement true? The point negative three, two belongs to the solution set of the inequality four ๐ฅ plus two ๐ฆ compared to negative two. (A) Greater than, (B) greater than or equal to, (C) less than, or (D) equals.
We have on one side of our inequality four ๐ฅ plus two ๐ฆ and on the other side negative two. And we need to determine what relation symbol goes here. To do that, we know that the point negative three, two makes the statement true. We also know that coordinates given in this form show the ๐ฅ-value and then the ๐ฆ-value. And that means we plug in negative three for ๐ฅ and two for ๐ฆ. Four times negative three is negative 12, and two times two is four. Negative 12 plus four is negative eight.
In order to find the right relation symbol, we need to compare negative eight and negative two. If we think about a number line with a zero, negative two is to the left of zero and negative eight is to the left of negative two. And that means we can say that negative eight is less than negative two. This means we could say that four ๐ฅ plus two ๐ฆ is less than negative two.
However, itโs possible that itโs also true that four ๐ฅ plus two ๐ฆ is less than or equal to negative two. But when we read the question carefully, we see that weโre only choosing between the four answer choices, and weโve only been given an option of less than. And that means, out of these four options, the best answer is less than. Four ๐ฅ plus two ๐ฆ is less than negative two.