Linear Equation using the Lowest Common Multiple

[CharlieDoggers]

Hey guys,

Sorry for having to post two days in a row but I've been struggling a bit with this section in my textbook - as some of the examples they use to solve the equations are a bit unclear. With the exercise question in the textbook here:



the textbook example (found at the bottom of this post) first says that cross multiplication is not possible between the two values that are divisible by 4 and 2 respectively due to the other values of 6x and 4 on the LHS, and so it says that you need to find the lowest common multiple between 4 and 12, which is 12 in this case, and multiply it throughout the formula which should (I believe) result in this:

12(6x) +12(4) + 12(x - 2 / 4) = 12(14 - 9x / 12)

But this is where I get confused. I interpret the textbook example to have the two values simplified by dividing the bottom value of the fraction by the LCM on the outside bracket (which also makes me wonder why these values aren't applied to the rest of the equation). So simplifying 12(x - 2 / 4) to remove the 4 below the top (and vice versa the other side) will result in the formula:

72x + 48 + 3(x - 2) = 1(14 - 9x) and with my attempts to solve it results in the answer x = - 28 / 78 which is clearly wrong as the answer in the textbook says - 1 / 3 (lmao).

I just want to know what errors I've made in the entire process?


Any help would be greatly appreciated


Textbook example:

 

[Cubist]

So simplifying 12(x - 2 / 4) to remove the 4 below the top...

NOTE: you need to group the numerator together with parenthesis when writing in text. Like this 12( (x - 2) / 4)

This is how the denominator is eliminated...

[math] 12\left(\frac{x-2}{4}\right) [/math]
[math]=\frac{12}{4}\left(x-2\right) , [/math] this step moves the denominator outside the parenthesis, since a*(b/c) = (a*b)/c = (a/c)*b

[math]= 3\left(x-2\right) , [/math] this step performs 12/4=3

If you need more explanation of the above then please ask.

72x + 48 + 3(x - 2) = 1(14 - 9x) and with my attempts to solve it results in the answer x = - 28 / 78 which is clearly wrong as the answer in the textbook says - 1 / 3 (lmao).

72x + 48 + 3(x - 2) = 1(14 - 9x) is correct. Please show us how you obtained x = - 28 / 78 since there's a mistake somewhere in that work.

 

[pka]

Hey guys,

Sorry for having to post two days in a row but I've been struggling a bit with this section in my textbook - as some of the examples they use to solve the equations are a bit unclear. With the exercise question in the textbook here:
View attachment 25125
72x + 48 + 3(x - 2) = 1(14 - 9x) and with my attempts to solve it results in the answer x = - 28 / 78 which is clearly wrong as the answer in the textbook says - 1 / 3

Charlie, I agree with the your textbook.
\(\begin{gathered}
72x + 48 + 3x - 6 = 14 - 9x \hfill \\
72x + 3x + 9x = 14 - 48 + 6 \hfill \\
84x = - 28 \hfill \\
x = \frac{{ - 1}}{3} \hfill \\
\end{gathered} \) SEE HERE

 

[Cubist]

OK, looking at pka's post, it seems probable that you(OP) got the sign of the "3x" term incorrect. I too used to get signs incorrect quite a lot. This will improve with practice. I recommend that you take a bit more time before you write "+" or "-" (double check the sign, until you become more experienced)

 

[CharlieDoggers]

Thanks a lot guys, you're all legends