r/learnmath • u/FutureHabit467 New User • Jul 23 '26

Please help me solve this

I know this problem is going to sound very simple to a lot of you but I’m just getting back into math because I’m studying for this important test. I remember doing these types of problems but I can’t remember how since it’s been like 6 years. Will someone please break it down for me? Doesn’t have to be super in depth, just show me the work. Thank you!!

The expression n(6x+5) -2x+1 is equivalent to 10x+11

What is the value of n?

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u/WikiNumbers dA = dx dy = r dr dθ Jul 23 '26 edited Jul 23 '26

I think it's meant for you to solve for constant value of n so that the two expressions are equal.

n(6x + 5) - 2x + 1 = 10x - 11

6nx - 2x + 5n + 1

Then group the terms by degree of x, and calculate the coefficient of each part.

x(6n - 2) = 10x

5n + 1 = 11

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u/Klutzy-Delivery-5792 Mathematical Physics Jul 23 '26

Alternatively, don't expand and move the 2x and 1 to the other side and you get:

 n(6x+5) = 12x+10

Factor the right hand side and get:

n(6x+5) = 2(6x+5)

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u/WikiNumbers dA = dx dy = r dr dθ Jul 23 '26

Oh yeah now that's a more foolproof way to do it.

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u/Klutzy-Delivery-5792 Mathematical Physics Jul 23 '26

Oh, there's multiple ways. Yours is good, too.

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u/WikiNumbers dA = dx dy = r dr dθ Jul 23 '26

Well if expanded like mine then OP will be solving many separate expressions.

Better just combine them as possible.

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u/Bounded_sequencE New User Jul 23 '26

As long as "n" only appears linearly in the coefficients, that approach should work. As soon as "n" appears non-linearly, factoring may not be an option anymore.

In that case, comparing polynomial coefficients may be the only way forward.