# given 12a-3(a+1)=a+1, what is the value of a?

#### eddy2017

##### Senior Member
given 12a-3(a+1)=a+1, what is the value of a?
this is a similar equation like the one i posted minutes ago, but I am at a loss here.
12a-3(a+1)=a+1
12a-3a-3=a+1
9a-3=a+1

I inserted this in an equation solver and got this:
(9a-3)+ (3-a)= (a+1) + (3-a)
what i don't understand is where the (3-a) is coming from.
thanks in advance for any help.
eddy

#### lev888

##### Elite Member
given 12a-3(a+1)=a+1, what is the value of a?
this is a similar equation like the one i posted minutes ago, but I am at a loss here.
12a-3(a+1)=a+1
12a-3a-3=a+1
9a-3=a+1

I inserted this in an equation solver and got this:
(9a-3)+ (3-a)= (a+1) + (3-a)
what i don't understand is where the (3-a) is coming from.
thanks in advance for any help.
eddy
Simplify by combining like terms. What do you get?

#### JeffM

##### Elite Member
To solve for a, you must "isolate" a on just one side of the equation.

$9a - 3 = a - 1 \implies$
$9a - 3 + 3 = a - 1 + 3 \implies$
$9a = a + 2 = 2 + a \implies$
$9a - a = 2 + a - a \implies$
$8a = 2 \implies WHAT?$
Questions?

Does the result check out when you insert your answer into the original equation?

#### eddy2017

##### Senior Member
I am gonna simplify it first. I have learned that is the first thing I need to see. if I can simplify it down a bit is better.

(9a-3)+ (3-a)= (a+1) + (3-a) I'll add sub (3-a) from both sides
9a-3+ 3-a -(3-a)= a+1 + 3-a - (3-a)
9a-3 = a+1 ( after canceling out)
now I'm adding 3 to both sides
9a-3 + 3= a+1 + 3
9a=a + 4 now subbin' a from both sides I get
9a-a= a+4-a
8a=4 dividing both sides by 8 I get
a= 4/8 simplyfin' further
a= 1/2

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#### eddy2017

##### Senior Member
To solve for a, you must "isolate" a on just one side of the equation.

$9a - 3 = a - 1 \implies$
$9a - 3 + 3 = a - 1 + 3 \implies$
$9a = a + 2 = 2 + a \implies$
$9a - a = 2 + a - a \implies$
$8a = 2 \implies WHAT?$
Questions?

Does the result check out when you insert your answer into the original equation?
Well, it gives me 1/2. Let me see if this checks out when I replace a for 1/2.

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#### eddy2017

##### Senior Member
Let me ask you all a question. if I want to check out this result of 1/2 I should replace a in the original equation for 1/2. that is a given. the original equation being 12a-3(a+1)=a+1
Can I change the 1/2 for 0.5 instead to make the checkin' out clearer?

If you notice I am editing a lot is because one of the things that the mod pointed out was that if I wanted to become a teacher I needed to write better, not like texting.

#### lev888

##### Elite Member
I am gonna simplify it first. I have learned that is the first thing I need to see. if I can simplify it down a bit is better.

(9a-3)+ (3-a)= (a+1) + (3-a) I'll add sub (3-a) from both sides
9a-3+ 3-a -(3-a)= a+1 + 3-a - (3-a)
9a-3 = a+1 ( after canceling out)
now I'm adding 3 to both sides
9a-3 + 3= a+1 + 3
9a=a + 4 now subbin' a from both sides I get
9a-a= a+4-a
8a=4 dividing both sides by 8 I get
a= 4/8 simplyfin' further
a= 1/2
Where did the first line come from? An equation solver? I wouldn't use it, especially if you didn't understand what it did. You got 9a-3=a+1. Continue from that.

#### Otis

##### Elite Member
9a-3=a+1

I inserted this in an equation solver
Why would you do that? You have solved equations of that form by hand in many of your threads over the past few years.

That equation solver looks like a waste of time, for a beginning algebra student.

#### Otis

##### Elite Member
lev, I must have picked up your vibes. We just cross-posted.

#### lev888

##### Elite Member
lev, I must have picked up your vibes. We just cross-posted.

Great minds.

#### eddy2017

##### Senior Member
Okay, I will retrace my steps and go from what lev said. I will post it later. Thank you. And thank you all for welcoming me back again. I am so sorry. But I have learned a lot. And you all are wonderful teachers!!!.

#### eddy2017

##### Senior Member
Where did the first line come from? An equation solver? I wouldn't use it, especially if you didn't understand what it did. You got 9a-3=a+1. Continue from that.
I put it in symbolab. I followed the process well, but when it comes to see if the result of 1/2 checks out is when I get stuck.
Trying to understand what equation softwares do is just because I am curious. I assume they are not wrong. Not at least for these type of equations. Of course, I understand I should solve it on my own and not rely on softwares.

#### Subhotosh Khan

##### Super Moderator
Staff member
I put it in symbolab. I followed the process well, but when it comes to see if the result of 1/2 checks out is when I get stuck.
Trying to understand what equation softwares do is just because I am curious. I assume they are not wrong. Not at least for these type of equations. Of course, I understand I should solve it on my own and not rely on softwares.
The better approach should be to solve with pencil/paper first,

#### lev888

##### Elite Member
I put it in symbolab. I followed the process well, but when it comes to see if the result of 1/2 checks out is when I get stuck.
Trying to understand what equation softwares do is just because I am curious. I assume they are not wrong. Not at least for these type of equations. Of course, I understand I should solve it on my own and not rely on softwares.
There is nothing wrong with experimenting with services like wolframalpha, etc. But in this case you started to solve an equation, put it into a solver, got from it something you don't understand (!), continued to solve it yourself. Makes no sense to me.

#### eddy2017

##### Senior Member
There is nothing wrong with experimenting with services like wolframalpha, etc. But in this case you started to solve an equation, put it into a solver, got from it something you don't understand (!), continued to solve it yourself. Makes no sense to me.
Le, I want to clear this up. While I agreed I had to continue solving it without the use of the software I totally understand the solution and steps involved. You said; 'got from it something you don't understand '. No, I did understand it!. What I had trouble with was when I went to check it out, replacing the a for the found value. I did not know how to check it out. That was what I meant. Anyway, I want to do it on paper now.
continuing where I left off; ( now on paper).
9a-3=a+1

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#### eddy2017

##### Senior Member
I can't turn the pic so it is straight. I hope you can see the work. Thank you all.

#### mmm4444bot

##### Super Moderator
Staff member
I totally understand the ... steps involved. You said; 'got from it something you don't understand '. No, I did understand it!
That's not what you'd said in your first post, Eddie:
got this:
(9a-3)+ (3-a)= (a+1) + (3-a)
what i don't understand is where the (3-a) is coming from.

#### eddy2017

##### Senior Member
Yes, the 3-a that the software used!!!. That is what I meant. And I did not understand it. But I knew the solution was 1/2 and when the tutors asked me to check the answer out I had trouble. That was all,mmm. I am trying to check it out now. I'll post my work. I have to replace a in the original equation by 1/2, right, and it has to check out, IF NOT, then I am doing something wrong.

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#### eddy2017

##### Senior Member
Checking it out now,
9a-3=a+1
9(1/2) - 3 = 1/2 + 1
solving fractions
3/2=3/2
it checks out.
Is this good?.
Thanks.

#### eddy2017

##### Senior Member
mmm, please, check post #12 and you will see where my doubt was. Please, I do not want any more misunderstandings.