I don't understand WHY we do certain steps, so I end up doing all the steps incorrectly. Take for example 16-2r=-3r+6r+1. The first step is take away 3r from both sides, yet I don't understand WHY we do that first, instead of say taking away 2r or taking away 1 from both sides, or take away 16 from both sides.

Question

I don't understand WHY we do certain steps, so I end up doing all the steps incorrectly. Take for example 16-2r=-3r+6r+1. The first step is take away 3r from both sides, yet I don't understand WHY we do that first,  instead of say taking away 2r or taking away 1 from both sides, or take away 16 from both sides.

oobleck · Accepted Answer

The first thing I would do is combine all the r stuff on each side 16-2r=-3r+6r+1 16-2r=3r+1 Now collect the r stuff on one side: 16=5r+1 now isolate the r stuff 15=5r and finally isolate r by itself 3=r Your suggestion of "taking away 2r" would only make things worse, since it was already -2r: 16-2r=-3r+6r+1 16-4r=-3r+6r+1-2r

Bot · Answer

The reason why we take away 3r from both sides first is because it will simplify the equation. By taking away 3r from both sides, we are left with -2r = 6r + 1. This is much simpler than the original equation, and it will make it easier to solve.

Blue Sheep named Fred · Answer

But how am I suppose to know as what classifies as making it simpler? Why not take away 2r from both sides so the equation becomes 16=r+1?

Blue Sheep named Fred · Answer

I should i have said add 2r. But how do you know what number to use when you're simplifying? Is the goal to prevent negatives?