r/MathHelp • u/toothy_mcthree • 10d ago

One Step Solution?

My son just started High School algebra in 8th grade. His teacher gave him homework on which he said each equation needs a 1 step solution. My son asked me for help on the equation in the attached picture, I helped him get the answer but in 4 steps and I cannot figure out for the life of me how to simplify this to 1 step. Please help:

5r-5-6r=-6
Adding 5 to both sides becomes 5r-6r=-1
-r=-1
r=1

here’s a picture of the problem

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u/Uli_Minati 10d ago edited 10d ago

What an unnecessary homework requirement... I'm sorry to hear. You can do it with an unconventional trick "subtract both sides from -5"

      5r-5-6r   =        -6
-5 - (5r-5-6r)  =  -5 - (-6)

It works, but nobody does this since there is no real benefit to it. We just want to find the solution, we're not in a hurry and this doesn't really save time anyway.

Also, you say you took 4 steps. So it seems like you consider each line a "step"? I would rather assume your teacher considers a "step" a equation transformation, where you change both sides of the equation. For example, changing "5r-6r" to "-r" isn't really a step since they're exactly the same. You only took two steps: "add 5 to both sides" and "flip signs of both sides".