# Thread: Absolute Value Equations

1. ## Absolute Value Equations

How, when you are given an absolute value equation, solve it graphically on a real-number line?

2. ## Re: Absolute Value Equations

Originally Posted by Bashyboy
How, when you are given an absolute value equation, solve it graphically on a real-number line?
You should know that the absolute value corresponds to the "size" of a number...

So say |x| = 3. That means that the size of the number is 3 units from 0. Therefore x = -3 or x = 3. Does that make sense?

3. ## Re: Absolute Value Equations

Yes, it does. But I become a bit more confounded with a problem like |x - 3| = 5. How would I solve one like this on a real number-line?

4. ## Re: Absolute Value Equations

Originally Posted by Bashyboy
Yes, it does. But I become a bit more confounded with a problem like |x - 3| = 5. How would I solve one like this on a real number-line?
Well that means that the size of x - 3 is 5 units from 0.

So $\displaystyle \displaystyle x - 3 = -5 \implies x = -2$ or $\displaystyle \displaystyle x - 3 = 5 \implies x = 8$.

5. ## Re: Absolute Value Equations

I have another problem. I am given a real number line with the two points -3 an 1 marked on it. How do I write an absolute value equations from this data?

6. ## Re: Absolute Value Equations

Originally Posted by Bashyboy
I have another problem. I am given a real number line with the two points -3 an 1 marked on it. How do I write an absolute value equations from this data?
If $\displaystyle a<b$ then the equation $\displaystyle \left| {x - \frac{{b + a}}{2}} \right| = \frac{{b - a}}{2}$ has solutions $\displaystyle x=a\text{ or }x=b$.

7. ## Re: Absolute Value Equations

I am truly sorry, but I don't quite follow. I have not seen anything like this before.

8. ## Re: Absolute Value Equations

Originally Posted by Bashyboy
I am truly sorry, but I don't quite follow. I have not seen anything like this before.
Are you saying that you cannot substitute $\displaystyle a=-3~\&~b=1$ into that?

9. ## Re: Absolute Value Equations

No, plugging and chugging is quite simple. But I have never seen that formula you have presented me with. Also, the way the book wants me to solve it is just graphically.