Solution to an equation: Determine whether x = 3/2 is a solution of 4x - 2 = 2x + 1

A

Algebob

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Hi everyone,


Please have a look at attached screenshot.


Once the variable has been substituted I multiply it, but my answers do not match the answer in the textbook on the side of the screenshot, nor do they equal.IMG_3240.jpg what am I missing?


first post. Thank you for your help.
 
This is my second Attempt, this time round, after multiplying the number to the fraction in the parenthesis, than I multiplied the whole number to the fraction…

IMG_3241.jpeg
 
On the first two attempts, you multiplied fractions incorrectly: [math]4\times\left(\frac{3}{2}\right)\ne\frac{4\times3}{4\times2}[/math]
How do you multiply a fraction by a whole number?

On the second, you also changed a subtraction and an addition to multiplications (and then did that wrong again).

On the third attempt, you put x in the wrong place, then forgot the order of operations. You can't do the subtraction, 4-2, and the addition, 2+1, before the multiplications.
 
Algebob said:
Hi everyone,


Please have a look at attached screenshot.


Once the variable has been substituted I multiply it, but my answers do not match the answer in the textbook on the side of the screenshot, nor do they equal.View attachment 36041 what am I missing?
Click to expand...
The product of [imath]4 = \frac{4}{1}[/imath] and [imath]\frac{3}{2}[/imath] is given by:

[imath]\qquad \left(\frac{4}{1}\right)\left(\frac{3}{2}\right)[/imath]

You seem instead of have multiplied the [imath]\frac{3}{2}[/imath] by [imath]\frac{4}{4}[/imath].
 
hi everyone, thank you for the feed back. I’ve taken your feedback into consideration and have attempted as follows and got the correct answer. Thank you.



IMG_3247.jpeg
 
Algebob said:
hi everyone, thank you for the feed back. I’ve taken your feedback into consideration and have attempted as follows and got the correct answer. Thank you.



View attachment 36047
Click to expand...
Good.

Even though what you've written here is mostly just a copy of what the source said (with the one step that you had trouble with added in explicitly), that is enough to show you do understand.

It's great that you weren't satisfied seeing an answer, but wanted to be able to work it out yourself. That's what we try to do here: not just give worked out answers, but give you a chance to do it. (Not everyone is as diligent about this understanding step as you ...)

You might be surprised how many students in algebra, or even calculus, have trouble with fractions. If this reminder wasn't all you need, you may want to review the topic on the side.
 
Have you not noticed that 4(3/2) = 12/8 = 3/2
You are saying that if you multiply a number, like 3/2, by 4 you get back 3/2. This is not true since only 1(3/2) = 3/2 and 4 is not 1. So you are multiplying wrong!
 
It is also easier to reduce before you multiply. You know that 4/2=2, so in 4(3/2) you reduce and get 2*3=6 (the 4/2 reduced to 2).

It becomes very beneficial to reduce in a problem like 3456(4/3456) where 3456(4/3456)=4 since the 3456/3456=1 and 1*4=4.
 
Algebob said:
Hi everyone,


Please have a look at attached screenshot.


Once the variable has been substituted I multiply it, but my answers do not match the answer in the textbook on the side of the screenshot, nor do they equal.View attachment 36041 what am I missing?


first post. Thank you for your help.
Click to expand...
4x-2=2x+1
4(3/2)-2=2(3/2)+1
12/2-2=6/2+1
6-2=3+1
4=4
 
Steven G said:
Since 4x-2=2x+1 is a linear equation why not just solve it for x.
4x-2=2x+1
2x=3
x=3/2
Yes, x=3/2 is the solution.
Click to expand...
Of course, the point of this lesson is to teach what it means for a number to be a solution, which is quite different from what it means to solve an equation. Students need to learn both how to find a solution, and how to check it.

So the answer to "why not" is "because that's not what they asked for ... or what they are evidently teaching".

And the problem said
1687832496865.png​
(not the solution), so what the lesson shows is exactly right. This method can't show that it is the only solution; but it isn't meant to.

god_is_atheist said:
4x-2=2x+1
4(3/2)-2=2(3/2)+1
12/2-2=6/2+1
6-2=3+1
4=4
Click to expand...
Copying exactly what the student wrote doesn't add much to the discussion.
 
Dr.Peterson said:
Of course, the point of this lesson is to teach what it means for a number to be a solution, which is quite different from what it means to solve an equation. Students need to learn both how to find a solution, and how to check it.

So the answer to "why not" is "because that's not what they asked for ... or what they are evidently teaching".

And the problem said
(not the solution), so what the lesson shows is exactly right. This method can't show that it is the only solution; but it isn't meant to.


Copying exactly what the student wrote doesn't add much to the discussion.
Click to expand...
I didnt actually read the whole thing but I do appreciate you pushing for integrity and content. I'll be more attentive in future posts.
 
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