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
