Math Help Forum: ALG-1 :: Writing and Graphing Compound Inequalities

First of all, I'd like to say hello, I'm new here. As you can probably tell by my post count. Secondly, Instead of just telling me answers could you (as in everybody) Guide me through the problem and explain each step? My teacher goes through everything rather fast and it is confusing to me.

Here is the first problem I'd like to go through:
Define a variable, write an inequality, and solve each problem.

The sum of three times a number and four is between -8 and 10.

I've always had a hard time with word problems, which is why I would like to go through them. First of all, what would my inequality be?

The first step is to get an algebraic expression before you try to write the inequality.

So choose a letter to represent your unknown number, e.g. . How would you write "The sum of three times this number and four" using algebra.

Well, this part I was pretty sure about. But If I'm wrong, I need work.

Originally Posted by AbstractHero

Well, this part I was pretty sure about. But If I'm wrong, I need work.

Between -8 and 10

wait a second...

So would I do this-
and

and then solve?

Originally Posted by AbstractHero

wait a second...

and

Wait a second what?

I'm confused with the next step.

Originally Posted by AbstractHero

I'm confused with the next step.

If 1 is between 0 and 2, how can we write that as an inequality?

Originally Posted by AbstractHero

wait a second...

So would I do this-
and

and then solve?

Yes, that is correct, though a more compact way of writing this is .

By the way, when you say "between -8 and 10", are we including the -8 and 10? If so, it should be ...

Originally Posted by Prove It

Yes, that is correct, though a more compact way of writing this is .

By the way, when you say "between -8 and 10", are we including the -8 and 10? If so, it should be ...

I don't think the word between is inclusive.

I should have been more clear. The sum of three times a number and four is between -8 and 10 is a problem I read straight out of my book, and I believe we are working on intersections and unions. This is exactly why it is confusing me.

We'll assume that the word between is not inclusive, so your inequalities are and .

How would you solve each of these inequalities for ?

Subtract the four, then divide by 3.

so that would get me the inequalities and

Also, if it has to be between -8 and 10 wouldn't the inequality signs be different?

No, they wouldn't be. And what you have written is correct.

Notice that this solution can be done as



(Subtracting 4)

(Dividing by 3).


So the more compact way of writing your final answer would be .

I don't get what you are saying. It has to be greater than or equal to -8, and less than or equal to 10.