WEBVTT
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So in this problem, we're being asked to solve
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the given inequality. And they were graft. The
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solution set on the number one. Well, I
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see we don't have any prophecies, so we don't
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have to worry about that. But we do have
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fractions. So remember to remove fractions, we're going
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to multiply both sides of our inequality by our least
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common denominator. Well, the least common denominator for
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two thirds and 1/4 is going to be 12.
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So we need to multiply both sides of our inequality
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by positive 12. So now let's go ahead and
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distribute Well, 12 times two thirds X is going
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to be eight X. Then we're gonna have 12
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times negative one, which is negative. 12.
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We'll bring down our in the quality sign greater than
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or equal to. Then we'll distribute the 12 on
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the right hand side. Well, 12 times one
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for effects is really just three X and then we'll
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have 12 times three, which is positive. 36
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. Perfect. Now we've gotten rid of our fractions
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, So the next thing we need to dio is
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collect are variable terms on one side of our equation
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. So to do this I'm going to subtract three
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x from both sides of our inequality. Well,
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eight X minus three X is five x so we're
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left with five. X minus 12 is greater than
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or equal to 36. So now we just have
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a two step. So we're going to start by
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adding 12 to both sides of our inequality. So
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we're gonna have 36 plus 12, which is 48
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. So we're left with five X is greater than
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or equal to 48. And then we'll divide both
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sides of our inequality by five. And because we're
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divided by a positive number, we don't need to
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change our sign. So we have X is greater
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than or equal to. Well, we can't reduce
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for the over five so we can leave that as
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our answer for the 8/5. Let me write that
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five. So it's a little bit more legible for
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us. Okay, so now we've solved our inequality
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. So we found that our answer is that X
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would have to be greater than or equal to 48
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5th. So now what we want to dio is
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graft, a solution set on a number line so
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to do that, we're going to start by making
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our number line. We're gonna put our key value
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, which in this case is 48 5th underneath.
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And in this case, we're going to use a
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close circle because our inequality sign is greater than or
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equal to, Which means that for the 8/5 is
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a solution, and because our inequality says X is
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greater than equal to 48 5th, all the values
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that would be greater than it will occur to the
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right hand side of this point. So we're going
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to shade the right hand side of our inequality.
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So now we have solved and graph the solution set
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for the given inequality.