How to Solve Algebra Problems Involving Variables and Equations?

[Cyrilshark]

Hey guys. So first off, I'm homeschooled. I have a math class every week though, but only being weekly, it's really easy to forget things my teacher explained and all, and in addition to that, I have a bad memory, and I resent math (or rather, numbers. ::P)

Alright, so I remember doing these two problems, and most of the time I can even remember most of the steps, but not all of them.

First:
0.06x + 0.24 - 0.02x = 0.36

So at first, I thought the x's resembled the next digit in the decimal, so the for first, it could be equal to 0.063, 0.068, etc. But after a few attempts trying to figure that out (I don't know the actual method of solving it, so I just threw random numbers as x, hoping to get close, and just slowly home into the answer, as it were. Anyways, that didn't work. Then I started to think the x meant multiplication, since a number with a variable immediately after it means to multiply, but that would work because of the addition sign before 0.24. So there's an example of what must be extremely simple, that I can't figure out.

Second:
y - (2y - 1) + 3 = 2y + 7

Here, I at first just tried different numbers as y, as I normally do when I can't figure it out, but after many failed attempts, I gave up. Then, after a bit, I decided maybe I should try moving some numbers to the other side. I know it sounds stupid, but it seems that's ALWAYS the answer when my teacher shows me how to do the problems I couldn't do. Anyways, so I subtracted 7 from the right, and added 7 to the left. And that's as far as I got. :P Because there wasn't really anything else I could've done. So, if you can help, it'd be appreciated, but if I didn't show enough that I attempted these, I completely understand.

Thanks!
Cyril

 

[Mark44]

Hey guys. So first off, I'm homeschooled. I have a math class every week though, but only being weekly, it's really easy to forget things my teacher explained and all, and in addition to that, I have a bad memory, and I resent math (or rather, numbers. ::P)

Alright, so I remember doing these two problems, and most of the time I can even remember most of the steps, but not all of them.

First:
0.06x + 0.24 - 0.02x = 0.36

This means 0.06 * x + 0.24 - 0.02 * x = 0.36.
There are two terms involving x on the left side, and one term on the left and one on the right that are constants.

Combine the two terms in x and add -0.24 to both sides, which results in:
0.04x = 0.12

Now divide both sides by 0.04 to solve for x.

So at first, I thought the x's resembled the next digit in the decimal, so the for first, it could be equal to 0.063, 0.068, etc. But after a few attempts trying to figure that out (I don't know the actual method of solving it, so I just threw random numbers as x, hoping to get close, and just slowly home into the answer, as it were. Anyways, that didn't work. Then I started to think the x meant multiplication, since a number with a variable immediately after it means to multiply, but that would work because of the addition sign before 0.24. So there's an example of what must be extremely simple, that I can't figure out.

Second:
y - (2y - 1) + 3 = 2y + 7

This is similar to the first problem.
Expand -(2y - 1) to get -2y + 1.
Combine like terms on the left side.
Move all the terms that don't involve y to the right side so that you have
<something> * y = <constant>
Divide both sides by whatever value <something> represents.

Here, I at first just tried different numbers as y, as I normally do when I can't figure it out, but after many failed attempts, I gave up. Then, after a bit, I decided maybe I should try moving some numbers to the other side. I know it sounds stupid, but it seems that's ALWAYS the answer when my teacher shows me how to do the problems I couldn't do. Anyways, so I subtracted 7 from the right, and added 7 to the left. And that's as far as I got. :P Because there wasn't really anything else I could've done. So, if you can help, it'd be appreciated, but if I didn't show enough that I attempted these, I completely understand.

Thanks!
Cyril

 

[Omega_Prime]

First:
0.06x + 0.24 - 0.02x = 0.36

So at first, I thought the x's resembled the next digit in the decimal, so the for first, it could be equal to 0.063, 0.068, etc. But after a few attempts trying to figure that out (I don't know the actual method of solving it, so I just threw random numbers as x, hoping to get close, and just slowly home into the answer, as it were. Anyways, that didn't work. Then I started to think the x meant multiplication, since a number with a variable immediately after it means to multiply, but that would work because of the addition sign before 0.24. So there's an example of what must be extremely simple, that I can't figure out.

Cyril

Hey Cyril, I think Mark pretty much covered everything but I wanted to chime in about coefficients as it sounds like you're just getting your pinky toe wet with Algebra.

The 0.06x from your first problem has two parts and you were correct in that they are multiplied together (the number and the variable, x) think of the number in front of it (commonly called the coefficient) as how much of "x" is there.

So for the equation 0.06x + 0.24 - 0.02x = 0.36 the first thing you'd want to do is combine like terms (terms with x in them can be combined, just pay attention to addition and subtraction), its all cake from there .

 

[Cyrilshark]

Thanks both of you for your time!
I'm sure I'll be seeing y'all around sooner or later :P :)