Solving Linear Equations: A Guide to Mastering Homework Problems

[nathan17]

Homework Statement

Solve these linear equations:

Homework Equations

$$\frac{x-4}{6} - \frac{x+5}{3} = \frac{4-x}{2}$$

The Attempt at a Solution

$$\frac{x-4}{6} - \frac{x+5}{3} = \frac{4-x}{2}$$
Multiplied by 6
$$\frac{6x-18}{6} - \frac{6x+30}{3} = \frac{24-6x}{2}$$
Simplified
$$x-18-2x+30 =12-6x$$
Group common terms
$$-2x+12=12-6x$$
Group common terms
$$4x+12=12$$
$$4x$$

I don't think, well I'm pretty sure it isn't right. I'm not sure when I've gone wrong. I can do simpler linear equations, but this has got me stumped. If anyone can provide any insight that would be great. I haven't done linear equations for a few years now.

 

[tiny-tim]

Hi nathan17!

$$\frac{x-4}{6} - \frac{x+5}{3} = \frac{4-x}{2}$$
Multiplied by 6
$$\frac{6x-18}{6} - \frac{6x+30}{3} = \frac{24-6x}{2}$$

Sorry, but this is a really silly way of doing it, because it's so likely to lead to a mistake (in this case, you've put 6 x 4 = 18)

To multiply (x+5)/3 by 6, just multiply the "/3" by 6 to give 2 (in your head), and then multiply the (x+5) by the 2.

 

[nathan17]

Sorry, but this is a really silly way of doing it, because it's so likely to lead to a mistake (in this case, you've put 6 x 4 = 18)

That's okay, I don't mind the feedback, good or bad, it all helps in the end! Heh, spend a few hours doing maths, you wouldn't think you would slip up on something so small..Sometimes it is the small things that get past though I guess.

What annoyed me a bit was that the book chapter on linear equations was only a few pages long, and didn't really go into much detail about equations like this one, so it made it a little bit difficult to understand what needed to be done.

If there is an easier way to go about this, I am open to suggestions because, after taking your advice, I still think I'm doing it wrong.

$$x-24 - 2x+10 = 12-6x$$
$$-2x-14 = 12-6x$$
$$4x-14=12$$
$$4x = 26$$
$$x = 6.5$$

Once again, I don't mind taking criticism for my work, otherwise, how else would I learn.

 

[tiny-tim]

Hi nathan17!

mmm … getting worse! ……

do it this way (and use brackets):

the (x-4) gets multiplied by 1, the (x+5) gets multiplied by 2, and the (4-x) gets multiplied by 3

(btw, are you sure it's x-4 and 4-x ?)

 

[nathan17]

Hi nathan17!

mmm … getting worse! ……

do it this way (and use brackets):

the (x-4) gets multiplied by 1, the (x+5) gets multiplied by 2, and the (4-x) gets multiplied by 3

(btw, are you sure it's x-4 and 4-x ?)

Haha, not only do I manage to not get the answer, but I get worse :P

Yeah, it's x-4 and 4-x.
I'm kind of afraid to post what I got because I know it's going to be wrong again lol.

$$(x - 4) - (2x + 10) = 12 - 3x$$
$$-2x + 6 = 12 - 3x$$
$$-2x = 6 - 3x$$
$$x = 6$$

If that's not right, maybe I should sleep on it and see how I go tomorrow. I think binary maths overloaded my brain a bit too much.

I hope I'm not frustrating you too much trying to explain it to me heheh

 

[tiny-tim]

he he

still wrong!

(x - 4) - (2x + 10) = -x + 6

Yes, get some sleep! :zzz:​

 

[nathan17]

he he

still wrong!

(x - 4) - (2x + 10) = -x + 6

Yes, get some sleep! :zzz:​

Haha. Okay, just to clarify. (x - 4) - (2x + 10) = -x + 6. That is because it's divided by 2?

 

[Mark44]

Haha. Okay, just to clarify. (x - 4) - (2x + 10) = -x + 6. That is because it's divided by 2?

There are two problems here.

1. The left side of the preceding equation does not simplify to -x + 6. You are partially ignoring the "-" in front of the second pair of parentheses.
2. One side of the original equation seems to have been lost in the shuffle.

Starting from the following equation, which is equivalent to the original equation, we have:
(x - 4) - (2x + 10) = 12 - 3x
x - 4 - 2x - 10 = 12 - 3x
-x - 14 = 12 - 3x
Can you continue from here?

 

[tiny-tim]

Haha. Okay, just to clarify. (x - 4) - (2x + 10) = -x + 6. That is because it's divided by 2?

Seriously …

get some sleep! :zzz: …

it'll all make sense in the morning! ​

 

[nathan17]

Starting from the following equation, which is equivalent to the original equation, we have:
(x - 4) - (2x + 10) = 12 - 3x
x - 4 - 2x - 10 = 12 - 3x
-x - 14 = 12 - 3x
Can you continue from here?

Okay, sorry about the late reply, been busy with study and everything.$$1(x-4)-2(x+5)=3(4-x)$$
$$(x-4)-(2x+10)=12-3x$$
$$x-4-2x-10=12-3x$$
$$-x-14=12-3x$$
$$-x = 26 - 3x$$
$$2x = 26$$
$$x = 13$$

Is that the solution to the problem?

 

[muso07]

That's exactly right. :)

 

[nathan17]

That's exactly right. :)

Haha! I just got the email saying there was a reply.. I was just about to post saying I give up, but finally, lol.. I have to say thanks to everyone here because, I really couldn't do it without the help.

I'm starting to get it now, hopefully by the time the test comes I will understand it more!