Question Video: Identifying the Point That Belongs to the Solution Set of a Given Inequality

Which of the following points belongs to the solution set of the inequality 8𝑥 + 3𝑦 ≥ −7? [A] (−3, 6) [B] (2, −8) [C] (−3, −1) [D] (−1, −8) [E] (−8, 9)

03:43

Video Transcript

Which of the following points belongs to the solution set of the inequality eight 𝑥 plus three 𝑦 is greater than or equal to negative seven? The options are (A) negative three, six; (B) two, negative eight; (C) negative three, negative one; (D) negative one, negative eight; or (E) negative eight, nine.

Well, if we take a look at our points, we’ve got 𝑥- and 𝑦-coordinates. So what we’re gonna do is we’re gonna substitute our 𝑥- and 𝑦-values into our inequality to see which one of our points actually satisfies our inequality. So first of all, if we look at (A) and substitute into the left-hand side of our inequality, we’re gonna get eight multiplied by negative three plus three multiplied by six. Well, this is gonna give us negative 24 plus 18, which is gonna be equal to negative six.

So then what we do is we see if it satisfies our inequality or negative six is greater than or equal to negative seven. So, yes, it does satisfy our inequality. So we can say that (A) belongs to the solution set of the inequality eight 𝑥 plus three 𝑦 is greater than or equal to negative seven.

But what we’re gonna do now is take a look at (B), (C), (D), and (E) to see if these also satisfy our inequality. So if we take a look at (B), we’re gonna have eight multiplied by two plus three multiplied by negative eight. This is the left-hand side of the inequality. That’s gonna give us 16 minus 24. And we get this because we’ve eight multiplied by two is 16 and then plus. And then we’ve got three multiplied by negative eight, which is negative 24. Well, if you add a negative, it’s the same as subtracting a positive. So you get, it’s 16 minus 24, which is equal to negative eight. Well, negative eight is not greater than or equal to negative seven. So it doesn’t satisfy our inequality. So therefore, we can rule out point (B).

So now if we take a look at point (C), we’re gonna have eight multiplied by negative three plus three multiplied by negative one, which gonna give us negative 24 minus three, which gonna be equal to negative 27. Well, once again, negative 27 is not greater than or equal to negative seven. So we can rule out point (C).

So now let’s move on to point (D). So for point (D), we’re gonna have eight multiplied by negative one plus three multiplied by negative eight, which is gonna give us negative eight minus 24, which is equal to negative 32. So if we take a look, we’ve got negative 32. Well, this is not greater than or equal to negative seven. So we can rule out point (D).

So it’s looking like point (A) is the only point that belongs to the solution set of the inequality eight 𝑥 plus three 𝑦 is greater than or equal to negative seven.

However, we’ll have a quick look at point (E). So what we’re gonna have is eight multiplied by negative eight plus three multiplied by nine, which is gonna give negative 64 plus 27. And this is gonna give the answer negative 37. Well, negative 37 is also not greater than or equal to negative seven. So we can rule out point (E).

So therefore, we can definitely say that the point that belongs to the solution set of the inequality eight 𝑥 plus three 𝑦 is greater than or equal to negative seven is point (A), which has the 𝑥-coordinate negative three and 𝑦-coordinate six.

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