what reson do i give to justify -5+(5+x)=-5+14 i dont understand this resoning stuff at all

Question

i dont understand this reasoning stuff its asking me to match the problems with the resoning like reflexive, inderect deductive resoning and things like that its a algebra plus class so please help i suck at these things

Answer 1

If you mean justify the solution, we can reason: Because there's a minus 5 (negative 5) on each side of the equation, then the only difference between the two sides is that there are brackets on the left and a number on the right where the brackets would be. Since it's an equation, meaning what's on the left equals what's on the right, the contents of the brackets must equal the number 14. So 5+x=14. That means that x must be 9 since it's the only number that added to 5 makes 14. In other words, x=14-5=9.

Another way to reason is to remove the brackets on the left exposing the contents. 5-5=0, leaving x on the left and the sum -5+14 on the right. -5+14 is the same as 14-5=9, making x=9 as before. Reversal of the operands in addition is the cumulative property of addition.