SOLUTION: Hi, I am learning about multiple-step equation in school and i am in Algebra-1. I was doing very well but up to this point i am confused and still don't know what i am doing wron

Question 12164: Hi,
I am learning about multiple-step equation in school and i am in Algebra-1. I was doing very well but up to this point i am confused and still don't know what i am doing wrong with my equations. We just started today and we are learning about the terms "all reals"(symbolized by an R w/ a line through it) and "no solution" (symbolized w/ an O with a slash{/} through it)Can you please help me understand what i am doing wrong with my equations. I really want to learn how so i won't be behind in my math class (lol sounds kinda nerdy but i really hoping and wanting to make a good grade in math this semester!:))
Here is an example of one of my questions:
2(4x+1)-x=7x+2
we are suposed to find out if the answer to X
*)has a solution...whole numbers only not fractions:)
*)is "all reals"...meaning x could be any possible number
OR
*)has "no solution"... which means it has no possible answer(that a whole #)
thanks for all of your help i'd really appricate it
:)
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
There are actually three types of equations to solve:
1. When you solve for x and get one or more solutions this is called a "conditional equation." This what usually happens, like when you solve x +3=5, the answer is x=2. This type of equation is called a CONDITIONAL EQUATION.
2. Sometimes when you solve for x, it so happens that all the x's subtract out, and a false statement results. For example, x+3 = 5 + x. If you subtract x from each side, you get 3=5, which is NOT possible. Therefore, there is NO SOLUTION, and that is where the answer is sometimes written with the greek letter phi (the circle with a line through it!). This type of equation is called a CONTRADICTION.

3. Sometimes when you solve for x, it so happens that all the x's subtract out, and a TRUE statement results. For example, x +3 = 3+x. If you subtract x from each side, you get 3=3, or maybe 0=0, which is ALWAYS TRUE. It's true no matter what x is, so this means the solution is all REAL values of x. This type of equation is called an IDENTITY.

In yur example,
2(4x+1)-x=7x+2
8x + 2 - x = 7x + 2
7x + 2 = 7x + 2

Subtract 7x from each side, and you get 2=2, which is always true. The solution is all real values, and this is called an IDENTITY.

R^2 at SCC
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