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).
