Question

Two questions I want to know:
1.How do you know if an equation is one solution, no solutions, or many solutions?
2.When working an equation with variables on both sides, if you know to divide,add,subtract,or multiply on one side, how do you know where to put it on the other side.


Equations:
1. 2x+3=2x+7
2. 2x+3=2x+3
3. 3(x+4)=3x+11
4. -2(x+3)=-2x-6
5. x+2x+3+4=5x+6x+7+8

Answer 1

Answer

for number 1.

when you are solving the algebraic problem if the variables are all canceled out and the equation does not equal then there is no answer but if it does equal and there's no variable then there is infinite answers

Step-by-step explanation:

Answer 2

1. if it has no solution, it means that the answer you got isnt equal so for example x+2(x+4)= 1 + 3(x+2), the answer you would get is 8=7. if it has one solution its just a normal answer so for example 2-3(x+2) =11, the answer would be x = -5. and if its many solutions the answer you get would be equal so an example is 3(x-4)-x = 2(x-6) and the answer you would get is -12=-12

2. i dont really know how to explain it but ill try- so if you’re trying to solve 5(x - 3) + 2x = 41 the first thing is to distribute and when you do that you get 5x - 15 + 2x = 41 but you have to combine the like terms so you would get 7x - 15 = 41 and you would want to get rid of the 15 so you would do -15 + 15 which equals zero but you have to put the +15 on both sides so you would also do 41 + 15. and another example is 5 + 2x -9 = 7x - 4 -5x, the first step is to combine like terms and you would get -4 +2x = 2x - 4 and you would want to get rid of the 2x so you would do - 2x on both sides and if you are trying to get rid of the variable on both sides you have to always put the thing youre dividing/adding/subtracting/multiplying with the other variable. (i really hope these answered your questions im not the best at explaining things so im sorry)


the answers to your equations are
1. No solution
2. Many solutions
3. No solution
4. Many solutions
5. -1 = x


hope this helped :)