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#1 2022-09-21 22:44:11

harpazo1965
Member
Registered: 2022-09-19
Posts: 29

Solve for a: Reviewing the Basics

Solve for a.

30 = 26 - (a/6).

I need to remove that fraction on the right for easy solving.

I will rewrite the equation this way:

30 = (26/1) - (a/6)

The LCD = 6. Multiply every term on both sides of the equation by 6.

6(30) = (26/1)(6) - (a/6)(6)

180 = 156 - a

180 - 156 = - a

24 = - a

24/(-1) = - a/(-1)

-24 = a

You say?

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#2 2022-09-21 22:58:53

ganesh
Administrator
Registered: 2005-06-28
Posts: 38,663

Re: Solve for a: Reviewing the Basics


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#3 2022-09-22 09:44:17

harpazo1965
Member
Registered: 2022-09-19
Posts: 29

Re: Solve for a: Reviewing the Basics

ganesh,

Are you saying that my way is too lengthy?
This is a math homework questions that one of
my kids couldn't solve. Is my way too lengthy for an 8th grader?

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#4 2022-09-22 12:50:21

ganesh
Administrator
Registered: 2005-06-28
Posts: 38,663

Re: Solve for a: Reviewing the Basics

Hi harpazo1965,

All I say is it can be solved in fewer steps.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#5 2022-09-22 15:08:45

Phrzby Phil
Member
From: Richmond, VA
Registered: 2022-03-29
Posts: 6

Re: Solve for a: Reviewing the Basics

Try undoing the operations in reverse precedence order to isolate the variable.


World Peace Thru Frisbee

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#6 2022-09-22 17:11:38

ganesh
Administrator
Registered: 2005-06-28
Posts: 38,663

Re: Solve for a: Reviewing the Basics

I think this too is not required. See this link:

Solving Equations

Introduction to Algebra.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#7 2022-09-22 22:02:32

Bob
Administrator
Registered: 2010-06-20
Posts: 9,515

Re: Solve for a: Reviewing the Basics

hi harpazo1965

Generally any solution is acceptable.  Many years ago I did some Advance Level marking for the UK EdExcel exam board.  There was one question that specified the method to be used and the chief examiner said any candidate who used another method should get no marks!  That is very unusual.

I would have used the same method as you but written less steps:

30 = 26 - (a/6)

(times by 6)

180 = 156 - a

(re-arrange)

a = 156 - 180 = -24

which is just 3 lines, same as Ganesh.

This equation is 'linear' meaning if you plot the graph y = 26 - a/6 you get a straight line.  The line y = 30 will cross it in just one place, so there is exactly one solution.  Sometimes you may spot a solution 'by inspection'.  It is acceptable to state this and then show it works:

I notice that -24 looks like a solution.

check 26 - (-24/6) - 26 + 4 = 30.  As this equation is linear this is the solution.  That's a two line answer smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#8 2022-09-22 22:32:51

harpazo1965
Member
Registered: 2022-09-19
Posts: 29

Re: Solve for a: Reviewing the Basics

ganesh wrote:

Hi harpazo1965,

All I say is it can be solved in fewer steps.

Ok. Thanks.

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#9 2022-09-22 22:34:39

harpazo1965
Member
Registered: 2022-09-19
Posts: 29

Re: Solve for a: Reviewing the Basics

Phrzby Phil wrote:

Try undoing the operations in reverse precedence order to isolate the variable.

Very good.

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