# Thread: Graphing on a number line Question

1. ## Graphing on a number line Question

Hello;

I'm sorry Im trying to learn to use Latex while simultaneously mastering precalc so far it's not working.

I'm currently going over, graphing numbers on a number line and my book is doing only a fair job in explaining specific rules.

I understand that; [1<4] but why do I have to write the answer as; 1< or equal to x < or equal to 4

$1\1eqx\1eq4$ if I can understand this reasoning, it would make the rest of my homework easier.

Thank You
Carolyn

2. Originally Posted by Carolyng66
Hello;

I'm sorry Im trying to learn to use Latex while simultaneously mastering precalc so far it's not working.

I'm currently going over, graphing numbers on a number line and my book is doing only a fair job in explaining specific rules.

I understand that; [1<4] but why do I have to write the answer as; 1< or equal to x < or equal to 4

$1\1eqx\1eq4$ if I can understand this reasoning, it would make the rest of my homework easier.

Thank You
Carolyn
Hello Carolyn,

I think, maybe, you're talking about "interval notation" and "set builder notation". Let's see if I can explain.

If you want to graph all the elements between and including 1 and 4, we can write the solution set in two ways.

Interval Notation: [1, 4]

The brackets mean the endpoints are included in the graph. Had they not been included, we would have used parentheses.

Set Builder Notation: $\{x | 1 \leq x \leq 4\}$

This is read "The set of all x, such that x is greater than or equal to 1 and less than or equal to 4".

Does this help? If not, post specific examples.

3. Originally Posted by Carolyng66
I understand that; [1<4] but why do I have to write the answer as; 1< or equal to x < or equal to 4
If you mean that you understand that the notation "[1, 4]" indicates the interval from 1 to 4 inclusive, but are wondering why you "have to write the answer" also in the form " $1\, \leq\, x\, \leq\, 4$", I think the reason is simply that you be able to understand the various notations.

Not all books use the same notation, so you need to be able to read each of them.