Number Lines: a quick refresher
If you are a visual person, the number line may be an especially useful tool for you! First let’s take a look at the number line:
Just as the name states, it’s…a line with numbers. They go in order from smallest to largest as you move left to right. The arrows indicate the line keeps going (and going) in both directions. The above number line shows -5 to 5, but I could have shown it going from -10 to 2, or -75 to 132, or -1003 to 2003. Number lines, like a great bread recipe, are quite versatile.
Who cares? Well, you might, because it can help you answer some GRE questions.
First a refresher.
y = 3
y can only be worth 3, so we put a big dot over the 3 to mark it.
y > 3
y is greater than or equal to 3, so it can be worth 3, but it can also be worth 4 or 5 or 240 or 238323. Wow! So by looking at the number line, you can see the least that y can be worth is 3, and it just goes up (and up and up) in value from there.
y > 3
What is different? Well now y can’t be worth 3, it has to be greater than 3. So we put a little donut hole over the 3, indicating that y can’t be worth that (hence the hole).
y < 3
y is less than or equal to 3, so it can be worth 3, but it can also be worth 2, or 0, or -192.
y < 3
y is less than 3, so it can’t be worth 3, but it can be worth 2, or -1, or -102.
Wow, we’ve gone over a lot! Here are some steps to graphing an inequality:
1. Look at the number in the inequality and graph that first. So for y > 3, look at the 3. Can y be worth 3? If so, put a big dot on the 3. If not, put a big donut hole on the 3.
2. Now pick a couple of numbers that y could be worth on one side of that dot or donut hole. So for y > 3, we know y could be worth 4 or 6. Now we know which direction to go on the number line.
3. Once you graph it, check your work. (Math, unlike life, gives you a chance to catch your mistakes). Looking at the inequality of y > 3, we say: y can’t be equal to zero. We check our number line and make sure that also shows that y can’t be zero. It does! That boosts our confidence.
Let’s say you are taking the GREs, and you need to know which is greater:
y > 5
Quantity A Quantity B
y 3
Well let’s make a number line.
Which is greater, Quantity A or Quantity B?
Looking at our number line, it’s clear that y will always be greater than 3. The answer is A.
More soon!