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Solving and Graphing Inequalities using Addition or Subtraction - Problem 2
Use the same rules to solving an inequality as you would solving an equation. To isolate the variable, use inverse operations. Once the variable is isolated and everything else is on the other side of the inequality sign, graph the solution on a number line. Remember: If the inequality is "equal to" a number, put a closed circle above that number. If the inequality is "greater than" or "less than" but not "equal to", then put an open circle above that number. Use an arrow to indicate all the values that fall within the inequality -- "greater than" or "greater than or equal to" means the arrow will indicate all the values above the number (to the right); "less than" or "less than or equal to" means the arrow will indicate all the values below the number (to the left).
Solving inequalities when you only have one variable or one letter is really similar to solving equations. You use the same ideas in that. If I want to get m all by itself, I'm going to have to do the same thing to this side of the inequality, as I do to this side. Right now m has that -3 going with it. The opposite of subtracting 3 is to add 3, so I'm going to add 3 to both sides and now it looks like 7 is greater than m.
That's it. That's my solution. I have m all by itself, and I can read this as 7 is greater than m or if you want to you could also rewrite this as m is less than 7. Those are the same thing just written in different formats. It's totally up to you which one want to go with, just make sure you read from left to right. That's the key.
One other thing I wanted to point out is that in the United States, most people make their sevens like this but it's kind of confusing because is that a 7 or is that a 7 or which one is the inequality sign, it's kind of tricky to read. Sometimes, in some places of the world, when they write their 7s they do a little slashy right there and in this case I think it helps, it makes it a little easier to tell that number is a 7, that's the inequality symbol. It's up to you if you want to do that. I think in the Math world that's pretty much accepted as 7or you could write 7as this. It doesn't matter but in this particular case I think the slashy helps make it more clear. Totally up to you.
Okay so we have our inequality; it's solved for m. Next thing we need to do is graph the solution. So I'm going to draw a number line and 7 is the important number. Since I have this symbol where there's no equality, it's just 7 is greater than m or m is less than 7, I'm going to do an open circle because 7 is not a solution to this situation. 7 gets a hole and I want to mark every single number that's smaller than 7, m is any number that's smaller than 7. And by drawing that arrow on the end I'm saying any number out towards negative infinity is a solution to this inequality, actually to this original inequality.
So when you come to a problem like this where it's just adding and subtracting, all you need to do is treat it as if you had an equal sign. Do the same thing to both sides of the equation. If you want to rewrite it like this you could and then be really careful when you're graphing about the open circle part or the closed circle part.