For the Arithmetically Inclined

[Duane Thomas]

A girl I know sent me this message:

"What is x/4-4=3x/4-6

I don't get how to solve these. Add 6 to both/ -1/4 to both??"

Anyone out there in the Enosverse better than me at math - which wouldn't be hard - want to help me out here? Please?

[ChuckS]

A girl I know sent me this message:

"What is x/4-4=3x/4-6

I don't get how to solve these. Add 6 to both/ -1/4 to both??"

Anyone out there in the Enosverse better than me at math - which wouldn't be hard - want to help me out here? Please?

x=4

[uscbigdawg]

X = 4

Rich

ETA: Eliminate the 4 by adding 6 to the left. Subtract X/4 from 3X/4 = X/2. Multiply both sides by 2. X = 4.

Edited September 11, 2008 by uscbigdawg

[ChuckS]

As they said in school: good but show work

The Problem: x/4 - 4 = 3x/4 - 6

add +4 to both sides:

x/4 -4 + 4 = 3x/4 -6 +4

x/4 = 3x/4 -2

multiply both sides by 4

4x/4 = 4(3x/4) - 2*4

x=3x -8

add -3 x to both sides

-2x = -8

divide both sides by -2

x=4

[Duane Thomas]

Can you give me a summary of the rules and the procedure that guides one through figuring of the problem?

[Duane Thomas]

Oops, ChuckS already did that.

But what leads to the conclusion to start with that we should add 4?

[uscbigdawg]

Duane,

Basically, get rid of the integers (the single digits w/ no 'x') as fast and as simple as possible. Then, get rid of the fractions as fast as possible (Chuck's example, multiply everything by 4). This could have been done first too. Then, reduce all your x's down to where you're left with some multiple of X and an integer and have them on opposite sides of the equation (the = sign). Then just divide.

Rich

ETA: Multiplication and division take precedence over addition & subtraction. So in your equation on the left side: x/4 - 4, you can't go x/4-4 = x/0. NO! (for multiple reasons) x/4 is divisible 'equation' waiting to happen and that takes precedence. If it was x/(5-4), then you could say x/(1) = X.

Hope that helped.

Edited September 11, 2008 by uscbigdawg

[ChuckS]

You can generally do things in different sequences but the main goal is to get the variable on the left side of the = and the rest of the crap on the right. In my simple mind, I thought that x/4 looked closer to the goal than 3x/4 so that is where I started.

In this game, if you do the same thing to both sides of the equality, you do not change the equality. So, you just keep doing stuff until it looks like you want it to look. Nothing really changes except in your perception and visualization of the equality. Maku Mozo Math

Edited September 11, 2008 by ChuckS

[uscbigdawg]

Okay...Chuck wins. Too much Maku Mozo for me.

Rich

[outerlimits]

i have a headache

[Duane Thomas]

Guys, would this be a good explanation to give her:

As much as posible to start, simplify the equation. A rule of thumb is to always do multiplication and division first, before addition and subtraction. In order to remind youself this is what you should do, it's helpful to change the way the equation is written by putting parentheses around the division/multiplication portions to separate them in your mind from the rest of the equation. HOWEVER if we can simplify the equation first with addition/subtraction, we'll do that before we "do multiplication/division first". Get rid of the integers (single numbers with no variables attached) first, then get rid of fractions. Remember, if you always do the same thing to both sides of the equals sign, you don't change the relationship of the two equations to each other. The eventual goal is to get a single number on one side of the equation, and a fraction on the other that is some multiple of the variable (in this case x). From there, you can just do simple division to figure out the variable.

So the problem is:

x/4 - 4 = 3x/4 - 6

Let's rewrite that as:

(x/4) - 4 = (3x/4) - 6

Then look at the problem. Since we have that - 4 out there, all by its lonesome, the easiest first step toward simplification is to get rid of that. Thus let's add +4 to both sides of the equation:

(x/4) - 4 + 4 = (3x/4) - 6 + 4

Or, put another way:

x/4 = (3x/4) * 2

Or, put another way:

x/4 = 6x/8

In order to get rid of the fraction (x/4) on the left side of the equation, at this point all we have to do is multiply both sides by 4. Thus:

x = (6*4)/8. In other words:

x = 24/8. In other words:

x = 4

There are numerous different ways to do any problem. Just remember:

Simplify.

Once you've simplified, multiply and divide.

Once you've multiplied/divided, then add/subtract.

Anything you do to simpify the equation on one side, you have to do on the other, as well.

Wind up with a variable on one side, and a fraction on the other, then divide to find the value of the variable.

[Flexmoney]

(x/4) - 4 + 4 = (3x/4) - 6 + 4

Or, put another way:

x/4 = (3x/4) * 2

[Pink Flyod vocie] Wrooong. Doit again.

[Nik Habicht]

Guys, would this be a good explanation to give her:

As much as posible to start, simplify the equation. A rule of thumb is to always do multiplication and division first, before addition and subtraction. In order to remind youself this is what you should do, it's helpful to change the way the equation is written by putting parentheses around the division/multiplication portions to separate them in your mind from the rest of the equation. HOWEVER if we can simplify the equation first with addition/subtraction, we'll do that before we "do multiplication/division first". Get rid of the integers (single numbers with no variables attached) first, then get rid of fractions. Remember, if you always do the same thing to both sides of the equals sign, you don't change the relationship of the two equations to each other. The eventual goal is to get a single number on one side of the equation, and a fraction on the other that is some multiple of the variable (in this case x). From there, you can just do simple division to figure out the variable.

So the problem is:

x/4 - 4 = 3x/4 - 6

Let's rewrite that as:

(x/4) - 4 = (3x/4) - 6

Then look at the problem. Since we have that - 4 out there, all by its lonesome, the easiest thing to do, to start, is to get rid of that. Thus let's add +4 to both sides of the equation:

(x/4) - 4 + 4 = (3x/4) - 6 + 4

Or, put another way:

x/4 = (3x/4) * 2 Right here's where you got into trouble --- this should read: x/4 = (3x/4) -2. All you've done is add 4 to each side, getting rid of the negative four on the left, and turning the negative 6 on the right into negative two.

Or, put another way:

x/4 = 6x/8

In order to get rid of the fraction (x/4) on the left side of the equation, at this point all we have to do is multple both sides by 4. Thus:

x = (6*4)/8. In other words:

x = 24/8. In other words:Cause 24/8 = 3, not 4.....

x = 4

From where you started to get into trouble:

x/4 = (3x/4) -2 Now your next move is to multiply both sides by 4, in order to get rid of those pesky quarters on each side. That requires you to multiply the entire side by 4, and looks like this:

x = 3x-8 Now you want to start moving things around so that the xs wind up on side and numbers wind up on the other. Since I have more xs on the right, I'll subtract an x from each side.

0 = 2x-8 Now I'll add 8 to each side to get the numbers on one side and leave the xs on the other.

8=2x You could have done the last two steps in either order --- I picked this particular way because you ended up with positive numbers on both sides --- sometimes that's easier for people.Now we'll divide both sides by 2 in order to solve for x

4 = x. Then to double check our answer, we plug 4 back into the original equation which now looks like this:

4/4 -4 = 3*4/4 - 6 =

1-4 = 3-6 =

-3 = -3

When I needed a college algebra grade in a hurry to get into nursing school last year, I bought a copy of Algebra for Dummies and it's workbook, and spent a week studying/working problems before taking the CLEP exam for college credit. If you ever had algebra, and need a refresher, that's a pretty inexpensive and fast method....

[Flexmoney]

(x/4) - 4 + 4 = (3x/4) - 6 + 4

adding 4 to negative 6 = negative 2

therfore:

x/4 = (3x/4) - 2

[Duane Thomas]

As much as posible to start, simplify the equation. A rule of thumb is to always do multiplication and division first, before addition and subtraction. In order to remind youself this is what you should do, it's helpful to change the way the equation is written by putting parentheses around the division/multiplication portions to separate them in your mind from the rest of the equation. HOWEVER if we can simplify the equation first with addition/subtraction, we'll do that before we "do multiplication/division first". Get rid of the integers (single numbers with no variables attached) first, then get rid of fractions. Remember, if you always do the same thing to both sides of the equals sign, you don't change the relationship of the two equations to each other. The eventual goal is to get a single number on one side of the equation, and a fraction on the other that is some multiple of the variable (in this case x). From there, you can just do simple division to figure out the variable.

So the problem is:

x/4 - 4 = 3x/4 - 6

Let's rewrite that as:

(x/4) - 4 = (3x/4) - 6

Then look at the problem. Since we have that - 4 out there, all by its lonesome, the easiest first step toward simplification is to get rid of that. Thus let's add +4 to both sides of the equation:

(x/4) - 4 + 4 = (3x/4) - 6 + 4

Or, put another way:

x/4 = (3x/4) -2.

Now in order to get rid of theneed to divide by four on the left side of the equation, we multiply both sides by 4. We wind upwith:

x = 3x -8

In order to get the -8 out of the equation, I'll add 8 to both sides.

Now you want to start moving things around so that the xs wind up on side and numbers wind up on the other. Since I have more xs on the right, I'll subtract an x from each side:

0 = 2x-8

Now I'll add 8 to each side to get the numbers on one side and leave the xs on the other. Which means:

8 = 2x

In other words:

4 = x (or, since we always love having X on the left):

x = 4

There are numerous different ways to do any problem. Just remember:

Simplify.

Once you've simplified, multiply and divide.

Once you've multiplied/divided, then add/subtract.

Anything you do to simpify the equation on one side, you have to do on the other, as well.

Wind up with a variable on one side, and a fraction on the other, then divide to find the value of the variable.

[AikiDale]

Hey! Hey! Hey!

I have not had to do that in over 40 years and I'd like to keep it that way alright?

"These forums are about the shooting."

Now where did I put that bottle of Ibuprofen?

[Duane Thomas]

How 'bout this:

So the problem is:

x/4 - 4 = 3x/4 - 6

Let's rewrite that as:

(x/4) - 4 = (3x/4) - 6

Then look at the problem. Since we have that - 4 out there, all by its lonesome, the easiest first step toward simplification is to get rid of that. Thus let's add +4 to both sides of the equation:

(x/4) - 4 + 4 = (3x/4) - 6 + 4

Or, put another way:

x/4 = (3x/4) - 2.

Now in order to get rid of the need to divide by four on the left side of the equation, we multiply both sides by 4. We wind upwith:

x = (3x) - 8

Now you want to start moving things around so that the xs wind up on side and numbers wind up on the other. Since I have more xs on the right, I'll subtract an x from each side:

0 = (2x) -8

Now I'll add 8 to each side to get the numbers on one side and leave the xs on the other. Which means:

8 = 2x

In other words:

4 = x (or, since we always love having X on the left):

x = 4

[ChuckS]

This is funny stuff! It's amazing what we will do when Sharyn is not streaming the nats...

[Nik Habicht]

As much as posible to start, simplify the equation. A rule of thumb is to always do multiplication and division first, before addition and subtraction. In order to remind youself this is what you should do, it's helpful to change the way the equation is written by putting parentheses around the division/multiplication portions to separate them in your mind from the rest of the equation. HOWEVER if we can simplify the equation first with addition/subtraction, we'll do that before we "do multiplication/division first". Get rid of the integers (single numbers with no variables attached) first, then get rid of fractions. Remember, if you always do the same thing to both sides of the equals sign, you don't change the relationship of the two equations to each other. The eventual goal is to get a single number on one side of the equation, and a fraction on the other that is some multiple of the variable (in this case x). From there, you can just do simple division to figure out the variable.

So the problem is:

x/4 - 4 = 3x/4 - 6

Let's rewrite that as:

(x/4) - 4 = (3x/4) - 6

Then look at the problem. Since we have that - 4 out there, all by its lonesome, the easiest first step toward simplification is to get rid of that. Thus let's add +4 to both sides of the equation:

(x/4) - 4 + 4 = (3x/4) - 6 + 4

Or, put another way:

x/4 = (3x/4) -2.

Now in order to get rid of theneed to divide by four on the left side of the equation, we multiply both sides by 4. We wind upwith:

x = 3x -8

In order to get the -8 out of the equation, I'll add 8 to both sides. I don't see this change anywhere in your explanation --- this whole line looks like it needs to be struck.....

Now you want to start moving things around so that the xs wind up on side and numbers wind up on the other. Since I have more xs on the right, I'll subtract an x from each side:

0 = 2x-8

Now I'll add 8 to each side to get the numbers on one side and leave the xs on the other. Which means:

8 = 2x

In other words:

4 = x (or, since we always love having X on the left):

x = 4

There are numerous different ways to do any problem. Just remember:

Simplify.

Once you've simplified, multiply and divide.

Once you've multiplied/divided, then add/subtract.

Anything you do to simpify the equation on one side, you have to do on the other, as well.

Wind up with a variable on one side, and a fraction on the other, then divide to find the value of the variable.

Last but not least --- check your work, by plugging your answer back into the original equation (in this case a 4 wherever an x appeared.) Does the match still work? Great -- you've solved the problem correctly. Math doesn't work? Problem somewhere....

[J-Ho]

What kind of girl would send you this!?!?!?!?!

A girl I know sent me this message:

"What is x/4-4=3x/4-6

I don't get how to solve these. Add 6 to both/ -1/4 to both??"

Anyone out there in the Enosverse better than me at math - which wouldn't be hard - want to help me out here? Please?

[Duane Thomas]

Okay, here's the proposed final draft:

As much as posible to start, simplify the equation. A rule of thumb is to always do multiplication and division first, before addition and subtraction. In order to remind youself this is what you should do, it's helpful to change the way the equation is written by putting parentheses around the division/multiplication portions to separate them in your mind from the rest of the equation. HOWEVER if we can simplify the equation first with addition/subtraction, we'll do that before we "do multiplication/division first". Get rid of the integers (single numbers with no variables attached) first, then get rid of fractions. Remember, if you always do the same thing to both sides of the equals sign, you don't change the relationship of the two equations to each other. The eventual goal is to get a single number on one side of the equation, and a fraction on the other that is some multiple of the variable (in this case x). From there, you can just do simple division to figure out the variable.

So the problem is:

x/4 - 4 = 3x/4 - 6

Let's rewrite that as:

(x/4) - 4 = (3x/4) - 6

Then look at the problem. Since we have that - 4 out there, all by its lonesome, the easiest first step toward simplification is to get rid of that. Thus let's add +4 to both sides of the equation:

(x/4) - 4 + 4 = (3x/4) - 6 + 4

Or, put another way:

x/4 = (3x/4) - 2.

Now in order to get rid of the need to divide by four on both sides of the equation, we multiply both sides by 4. We wind up with:

x = (3x) - 8

Now you want to start moving things around so that the xs wind up on side and numbers wind up on the other. Since I have more xs on the right, I'll subtract an x from each side:

0 = (2x) -8

Now I'll add 8 to each side to get the numbers on one side and leave the xs on the other. Which means:

8 = 2x

In other words:

4 = x (or, since we always love having x on the left):

x = 4

In order to check your answer, plug 4 into the original equation in place of x:

(4/4) - 4 = (3*4/4) - 6

Which leads us to:

1 - 4 = (12/4) - 6

Which leads us to:

-3 = 3 - 6

Which leads us to:

-3 = -3

Since -3 does indeed equal -3, thus x must = 4

There are numerous different ways to do any problem. Just remember:

Simplify.

Once you've simplified, multiply and divide.

Once you've multiplied/divided, then add/subtract.

Anything you do to simpify the equation on one side, you have to do on the other, as well.

Wind up with a variable on one side, and a fraction on the other, then divide to find the value of the variable.

[Duane Thomas]

What kind of girl would send you this!?!?!?!?!

A woman with a 135 I.Q. helping her son with his homework.

[AikiDale]

Ah Ha!

Some people will do anything to impress a girl....

ETA: Although it makes my head hurt (there is a reason I was an English/Journalism Major) it is nice to know once again it matters not the subject, one can pose a question on these forums and get reliable information quickly from knowledgeable folks in a kindly manner.

Edited September 12, 2008 by AikiDale

[Nik Habicht]

Duane,

good job! Hope it lands you a second date --- for all that effort....

[SiG Lady]

Reminds me of first-year Algebra. God, how I loved it!