What are Some Examples of Infinite Value Problems in Algebra?

[deficiency4math]

Hi,

I was wondering if anyone could help me with these infinite value questions that I really don't get...

stuff like this:

|2x+4| = 16

or

|10x| + 5 = 40

(i made these questions off the top of my head, so they might not work out properly and nicely)

Thanks

 

[matt grime]

Are you only looking for answers where x is a real number? Since there are only at most two answers.

|y|= r if and only if y=r or y=-r.

If you're talking abuot C or some other space, just say so and someone will explain what to do there.

 

[arildno]

You do mean "absolute value", right?
The way to solve these questions is:
1) Determine the different x-intervals in which the expression inside a given absolute value signs are positive or negative.
For example, for your second case we have:
$$10x<0\to{x}<0, 10x\geq0\to{x}\geq0$$
Hence, you have two distinct regions two consider: x less than 0 and x greater than (or equal to) zero.

2) See what solutions exist, if any, on each region:
In your second case:
a)$$10x<0:$$
Here, 10x<0, so |10x|=-10x.
Thus, we must check if we have actual solutions satisfying: -10x+5=40
Rearranging terms, we get $$x=-3.5$$
Since -3.5<0, this represents a true solution, since x must be negative in this region.

b)$$10x\geq0$$
Here, |10x|=10x, thus we must check if we have solutions of: 10x+5=40
and we see that x=3.5 works.
Get it?
EDIT:
If you are to find solutions where you have nummerous addends in the form of absolute values, just split up your analysis in the appropriate manner.

 

[deficiency4math]

thanks a bunch