Question 1

so it is x=-16?

Accepted Answer

Yes, but as I saw the comment from a year ago the same thought popped up in my head. Where are you know. Your comment was from 9 years ago, and your description saws you were 14 so you would have to be 23, or so. Time flies, wow

Question 2

can you multiply the denominator on both sides

Accepted Answer

If you multiply both sides by an integer, it's always multiplying the numerator and therefore making the number larger. If you did otherwise, by multiplying the denominator, then the number would be smaller, which is rather a division. I hope my explanation makes sense and is helpful.

Question 3

I am struggling on how to transfer varibles to one side of the equation. Any tips?

Accepted Answer

Hi, Rebecca;

*Transferring Variables*
Transferring variables might look like a complex subject to tackle at first glance, but it actually proves itself to be much simpler--you just need to _understand_ it.

In an equation, the *left hand side* (LHS--the left expression) and the *right hand side*  (RHS--the right expression) are equal. Now, a very significant tip to take note is that _since both sides are equal, both must be treated equally_. But how do we do that?

Here is an example:
Billy has two baskets of equally filled apples. The left basket has 2 packs of 4 apples and 2 pears while the right basket has 3 packs of 2 apples and 2 pears. On the way home, Billy decided to eat 3 fruits from each basket. How many fruits are left in each basket?
```2(4+2)=3(2+2)```
I've done the equation for the original number of fruits in each basket, but after Billy took 3 from each basket, I am left to modify my equation. But how do we do that?
```2(4+2)-3=3(2+2)-3```
We subtract 3 from both sides! This would mean that both baskets, being originally equal, would still be equal when Billy goes home to eat the rest.
```2(4+2) -3 =3(2+2) -3
2(6)-3=3(4)-3
12-3=12-3
9=9
∴ There are 9 fruits left in each basket```

Now what does this have to do with *transferring variables*? Transferring variables are basically like what we did above, except they're not numbers yet.

This time, let's say we don't actually know how many pears there are  in each pack, considering the fact that the number of pears are equal in all of the packs in both baskets.
```2(4+x)=3(2+x)```
First, let us *simplify* the equation.
```2(4+x)=3(2+x)
8+2x=6+3x```
Here we are--transferring variables! This time, think about what we did to the equation when Billy decided to eat 3 fruits from both baskets; we subtract the variable from both sides!
```8+2x=6+3x
8+2x -3x =6+3x -3x
8+2x-3x=6```
Notice that when we transfered `3x` from the RHS to the LHS, it turned *negative*. When we transfer variables to the other side, its sign becomes opposite! That's how easy it is!
Now, let's solve the equation!
```8+2x-3x=6
2x-3x=6-8
-x=-2
-1(-x)=-1(-2)
x=2
∴ There are 2 pears in each pack.```
Ta-da! The same equation!

(Sorry if I was very lengthened about such a simple subject. I like to explain thoroughly)

Question 4

in the test i got the problem...

16 - 2t = 3/2t + 9

and i converted the fraction to the decimal 1.5
so...

16 - 2t = 1.5t + 9
-16                -16

-2t = 1.5t - 7
-1.5t  -1.5t

0.5t = -7
i devided both sides by 0.5 and got -14, so i punched the answer in and they said the correct answer was actually 2. what did i do wrong?

Accepted Answer

hello, so what you did wrong was simply a subtracting mistake. you can totally just convert your fraction into a decimal and it will still work.  So lets start from the beginning,

16 - 2t = 3/2t +9

so you convert the fraction into the decimal

16 - 2t = 1.5t + 9
 then you subtracted 16 from both sides which is right,

16 - 2t = 1.5t +9 
-16                       -16

-2t = 1.5t -7

you were right up to this step. now we subtract 1.5t from both sides

-2t = 1.5t -7
-1.5t -1.5

you get...
-3.5t = -7
which equals 2!

so you only messed up in the step where you add a -2t to a -1.5t.
if you do not understand why we add these together look at Khan's video "adding negative numbers example"

hope this helps

Question 5

Another way to solve this "quickly" is this: 3/4x+2=3/8x-4, what number you need to multiply 3/4x for so denominator becomes 8 as well?

You multiply by 2 and get 6/8x+2=3/8x-4

1st step 6/8x-3/8+2=3/8x-3/8x-4
2nd step 3/8x+2-2=-4-2
3/8x/3/8=-6/3/8 (0.375)

x=-16

Accepted Answer

The third step is much easier to multiply by the reciprocal rather than dividing, so
3/8  x • 8/3 = 6 • 8/3, since 6/3 =2, you get 16 faster.
If you are going to do it quickly, try doing everything as simply as possible, but this is great for those not afraid of fractions.

Question 6

I still didn't understand where the 8 came from, can someone please explain it again differently? How do you get to that conclusion?

Accepted Answer

The 8 is the lowest common multiple of the 2 denominators (4 and 8).  Use the same process you would use to select the smalles common denominator for those 2 fractions.
Multiples of 4: 4, 8, 12, 16, etc.
Multiples of 8: 8, 16, 24, etc.
The first multiple in common is 8.

Hope this helps.

Question 7

my question is how do you solve this problem with one fraction?

Accepted Answer

The general rule for solving equations with fractions — whether it be only on one side or both — is to try to get rid of all of them. The most common way to find the lowest common multiple (LCM) of all of the fractions, and then multiply the LCM on both sides of the equations.

hopefully that helps :)

hopefully that helps :)

Question 8

what if in a question there is only one fraction on one side.

Accepted Answer

That's ok.  If you want to eliminate the fraction, you can multiply the equation by the denominator of the fraction.  Or, equations can be solved just doing the math with the fraction.   Most people choose to eliminate the fraction because the work steps are then a little simpler to complete.

Class 7

Course: Class 7 > Unit 6

Equation with variables on both sides: fractions

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