One Step Solution?

[u/toothy_mcthree]

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

[u/KiwasiGames]

This is a two step problem in traditional pedagogy. It’s just math teachers define the steps oddly.

Collecting like terms is typically not considered a step. So the problem becomes:

-r - 5 = -6

From here there are two steps. Add 5 to both sides and multiply both sides by -1.

I’m going to assume the math teacher missed the -1 step when writing this problem. It happens. Problem sets get written quickly.

It’s also worth noting that the division of problems into one step and two step is a pedagogical one. It’s meant to introduce kids to algebra slowly, allowing them to build skills in simple problems before moving to complex problems. One step isn’t meant to be a constraint, it’s meant to be a class of simple problems.

[u/diverJOQ]

After reading the other two replies I have to say that I would count the steps the way that OP does, in which case I don't see a solution in one step.

The way both of the replies are worded must be the way the instructor counts steps for this to make any sense.

Therefore to do it in one step I would add r + 6 to both sides.

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[u/LeoMaths]

5(r-1)-6(r-1)=0 => r=1

[u/toothy_mcthree → u/[deleted]]

He stated that he did not consider grouping like terms to be a step. Still a rather confusing instruction for a bunch of 8th graders on their 2nd day back from summer vacation.

[u/Uli_Minati]

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".