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 𝑥 plus two 𝑦 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 𝑥 plus two 𝑦 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 𝑥-value and then the 𝑦-value. And that means we plug in negative three for 𝑥 and two for 𝑦. 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 𝑥 plus two 𝑦 is less than negative two.
However, it’s possible that it’s also true that four 𝑥 plus two 𝑦 is less than or equal to negative two. But when we read the question carefully, we see that we’re only choosing between the four answer choices, and we’ve only been given an option of less than. And that means, out of these four options, the best answer is less than. Four 𝑥 plus two 𝑦 is less than negative two.