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Solve Inequalities Using Addition and Subtraction - Example 1

In mathematics, an inequality is a statement that one number is greater than or less than another number. The notation a ? b means that a is less than or equal b. The notation a ? b means that a is greater than or equal to b. If the two numbers have the same sign, the relationship is positive (or less-than) and if they have different signs, the relationship is negative (or greater-than).

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McMaster University

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So in this example, we're being asked to salt to given inequality. And then we're going to graft the solution set on a number one. Well, remember, solving inequalities is just like solving equations. So the first thing we need to do is isolate are variable. So the move, the three to the right hand side of our inequality. We're going to subtract three from both sides because three minus three is zero. So these terms cancel out. So now we're left with X is less than while negative eight minus three is negative a weapon. So now we've solved our inequality. So what we found is that X is any number that's less than negative 11. But remember, not equal to negative 11 now, the second thing they want us to dio is graft, a solution set on the number line. Now, the one thing that you typically do when you set up a number line is usually put zero in the middle and you put tick marks up until you get to the numbers you need. But you'll find sometimes we might have answers that air really big, like maybe the answer is 200. You certainly wouldn't want to make a number line that that's large, that large. So here's what you need to dio You can just set up your number line. The important number that you need here is our critical number, which is negative. 11. So I'm gonna put a tick mark in the middle and label it negative 11. And what it implies is that any value to the left of it is less than, and any value to the right of it is greater than which is exactly what a regular number line means. Now some people will put in the values just greater than just lesson, which is perfectly fine. But you don't have thio. So remember to graph X is less than negative 11 on the number line. The first thing we need to figure out is, should this be an open or close circle? Well, because negative 11 is not a solution. That means we should have an open circle. So we're gonna have a open circle at negative 11. And because our values of X have to be less than negative 11, our values that would be less than negative 11 would happen to the left of negative 11. So on our number line, we're going to shade in the left hand side of our number line and now we have graft. A solution set to represent X is less than negative 11.

Syracuse University
Top Algebra Educators
Alayna H.

McMaster University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University