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Can someone help me solve this Algebra 2 problem?

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2a - 3b = ac + 7

Solve for a.

My son has this problem and another that is similar, and I don't know how to solve for a. I could totally do this if it were solve for b or c. Can the a be isolated and if so, please tell us how.

Thanks!

If you are kind enough to help, explain it as if we know nothing- you won't hurt my feelings!

2a-3b = ac+7

2a-3b-ac = 7

2a-ac = 7 + 3b

a(2-c) = 7 + 3b

a = (7+3b)/(2-c)

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2a-3b = ac+7

2a-3b-ac = 7

2a-ac = 7 + 3b

a(2-c) = 7 + 3b

a = (7+3b)/(2-c)

Thank you! It makes perfect sense now that I see it worked out! Hopefully I can apply it to the other problem.

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As a general strategy:

identify all the terms that have a in it (for beginners, using colored pencil can be helpful)

move all the terms with a to one side

move all the terms that do not have an a in them to the other side

Look at the side with the a and see if you can factor it out (which you always can if a occurs only linearly, not squared, cubed or to higher powers)

Edited by regentrude
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As a general strategy:

identify all the terms that have a in it (for beginners, using colored pencil can be helpful)

move all the terms with a to one side

move all the terms that do not have an a in them to the other side

Look at the side with the a and see if you can factor it out (which you always can if a occurs only linearly, not squared, cubed or to higher powers)

Yeah, that last step is where we got hung up. Forgetting that the a could be factored out via what we jokingly call "undistributing".

Thanks for the explanation in words. I think it will help my son to have that listed as a reminder.

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You guys are great teachers! He and I were both able to work the second problem we had trouble with based on what we learned from you.

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You guys are great teachers! He and I were both able to work the second problem we had trouble with based on what we learned from you.

I am saying this very gently and hope you are not offended:

you say this is "algebra 2". This material should have been covered in algebra 1 during the first few months. I would be a bit concerned about his readiness for algebra 2 if he has forgotten how to solve linear equations with one variable.

Edited by regentrude
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I'm not offended. This is the second day of Alg.2 and still review. It has been over a year sicnce Alg 1 because we did geometry in between. Also, a new curriculum that does things a little differently.

I am, for now, considering it rusty skills. Once he was reminded, he used the same skill to do the other problem with no trouble.

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