Question

Can someone give me a only letter equation to solve?

Answer 1

2x+3=11

Answer 2

take 3 from both sides getting 2x=8
divide both sides by 2 gettin x=4

Answer 3

Btw, grats on Master rank

Answer 4

Can i have a harder one now?

Answer 5

good job

Answer 6

that's called only a letter equation? :D

Answer 7

Nope but i take whats coming lol

Answer 8

Let's do a slightly trickier one: (1/3)x+2=3

Answer 9

Ill take (1/3)x+2=3
1x+6=9, right sofar?

Answer 10

That's right thus far!

Answer 11

x+6=9
x=3

Answer 12

?

Answer 13

That's correct.

Answer 14

Very good! Let's do this one now: (2/3)x+(5/2)=(5/4)

(I love fractions.)

Answer 15

Please put that in equation form

Answer 16

\[\frac{2}{3}x+\frac{5}{2}=\frac{5}{4}\]

Answer 17

If you can do that without problems, then you would have mastered the solving of single-variable, linear equations. :P

Answer 18

Hmm

Answer 19

Im supposed to "equalize the fractions" right?

Answer 20

Wait!

Answer 21

We're trying to solve for \(x\), so try and use the properties of addition, subtraction, multiplication and division to achieve that!\[\]

Answer 22

NONONONO

Answer 23

no clues :(

Answer 24

(2/3)x+(5/2)=(5/4)----->(4/6)x+(10/4)=(10/8)?

Answer 25

No that cant be it..

Answer 26

wait, just say yes or no, not why.

Answer 27

You rewrote the equation. :P

Answer 28

(2/3)x+(5/2)=(5/4)
(2/3)x=(5/4)-(5/2)
Right so far?

Answer 29

Yes

Answer 30

Now multiply both sides by 3 to get (3/3)x=(5/4)-(5/2)*3?

Answer 31

If so i have the answer

Answer 32

You have the right idea, but you're overlooking a few steps. :)

Answer 33

(3/3)x=(5/4)*3-(5/2)*3??

Answer 34

Let's first focus on trying to simplify this:\[\frac{5}{4}-\frac{5}{2}.\]Can you do that?

Answer 35

5-5
----
4-2?

Answer 36

There's where we're getting stuck. :P

You need to learn how to simplify expressions of the form\[\frac{a}{b}\pm\frac{c}{d}.\]

Answer 37

:( i thought i knew this stuff...

Answer 38

It's not too bad, really, there's a simple rule which states that\[\frac{a}{b}\pm\frac{c}{d}=\frac{ad\pm bc}{bd}.\]

Answer 39

Whats the logic in that?

Answer 40

To put it simply, you cannot add nor subtract fractions with different bases. In other words,\[\frac{5}{4}-\frac{5}{2}\]cannot be simplified as it stands since they have different bases (4 and 2).

Answer 41

So i need to find the greates common (something i cant remember)?

Answer 42

However, if you have something like\[\frac{3}{2}+\frac{5}{2},\]they have similar bases and thus you can add them accordingly:\[\frac{3+5}{2}=\frac{8}{2}=4.\]

Answer 43

You can do that OR you could use the fact that\[\frac{a}{b}\pm\frac{c}{d}=\frac{ad\pm bc}{bd}.\]

Answer 44

How about if they have similar (the ones we have over the base)(whatever they call them)

Answer 45

The numerator? Do you mean something like\[\frac{3}{5}+\frac{3}{6}?\]

Answer 46

yeah

Answer 47

Oh wait, never mind i think i see why that wont work

Answer 48

It doesn't matter: they have different bases and you can't add them.

Answer 49

(2/3)x=(5/4)-(5/2) 5*2-4*5/2*5?

Answer 50

I saw something I liked: you know how to manipulate fractions. Could you manipulate\[\frac{5}{4}-\frac{5}{2}\]so that they have similar bases?

Answer 51

Im not sure i know what you mean by manipulate

Answer 52

You mean

Answer 53

make them higher so they match or something?

Answer 54

With "manipulate" I mean to say "play with" or "rearrange," like this:\[\frac{5}{2}=\frac{10}{4}=\frac{15}{6}=etc.\]

Answer 55

Oh you did mean like that

Answer 56

(5/2)
(5/4)-------->2.5/2?

Answer 57

Aw man.. im really worthless at this..

Answer 58

At this rate ill never learn quantum physics..

Answer 59

That's good! But try and make the bases of the two fractions match and try to have only whole numbers in both the numerator and denominator.

Answer 60

Well how? i cant go upward.

Answer 61

(5/2)---->(10/4)!!!!
(5/4)

Answer 62

Now i can have (15)/(4)

Answer 63

I'll give you an example. I'm given\[\frac{7}{3}+\frac{4}{5}.\]I want their denominators match, so I multiply \(7/3\) by \(5/5\) to get \(35/15\), and I multiply \(4/5\) by \(3/3\) to get \(12/15\). They now have similar denominators and I can add them:\[\frac{35}{15}+\frac{12}{15}=\frac{47}{15}.\]

Answer 64

So i wasnt right?

Answer 65

Very good! You converted\[\frac{5}{4}-\frac{5}{2}\]into\[\frac{5}{4}-\frac{10}{4}.\]What's the next step?

Answer 66

(2/3)x=(5/4)-(10/4)
(2/3)x=(10-5)/4?

Answer 67

That's very close! But you switched the signs:\[\frac{5}{4}-\frac{10}{4}=\frac{5-10}{4}.\]

Answer 68

Oh right! so its (2/3)x=(-5)/4

Answer 69

That's correct! Now, let's solve for x. :)

Answer 70

Can we multiply both sides by 3 now?

Answer 71

Yes we can. :)

Answer 72

(3/3)x=(-5)/4*3

Answer 73

x=(-5)/4*3

Answer 74

Is it right? :D

Answer 75

Well, let's look at the LHS only: when you multiplied\[\frac{2}{3}x\]by \(3\), you somehow got\[\frac{3}{3}x.\]How did this happen?

Answer 76

Wait, should i divide both sides by 2/3?

Answer 77

x=(-5)/4*(2/3)

Answer 78

Please say its right..

Answer 79

You could do that, yes, but let's do it one step at a time first so that you understand the process. When you have\[\frac{2}{3}x,\]to get rid of that \(3\) in the denominator, we DO multiply the fraction by \(3\) so that this happens:\[\frac{2}{3}x\implies3\cdot\frac{2}{3}x\implies\not{3}\cdot\frac{2}{\not{3}}x\implies2x.\]

Answer 80

Oh right, i knew it had something to do with multiplying with the denominator!

Answer 81

Now, let's do a cool little trick: what happens if I multiply\[\frac{2}{3}x\]by\[\frac{3}{2}?\]:)

Answer 82

5/5?

Answer 83

Close!\[\frac{3}{2}\cdot\frac{2}{3}x=\frac{6}{6}x=x.\]

Answer 84

so essentially, i was right?

Answer 85

Now, can you apply this to solve\[\frac{2}{3}x=-\frac{5}{4}?\]

Answer 86

Yes, you were right, but I don't think you understood the whole process, which now you do. :)

Answer 87

Both sides multiplied by 3/2?

Answer 88

That's correct.

Answer 89

x=11/4

Answer 90

If thats not right, im gonna go give up on physics and go cry in a corner..

Answer 91

I think you got it already, but you're trying to speed your way through it. Take your time! :)

Let's check again:\[-\frac{5}{4}\cdot\frac{3}{2}=?\]

Answer 92

-5/4*6/4 so 1/4?

Answer 93

I see what you're trying to do, but remember that multiplication and division of fractions is totally different from addition and subtraction. :) They're easier, in fact!\[\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd}.\]

Answer 94

-30/4?

Answer 95

Look at our final expression:\[-\frac{5}{4}\cdot\frac{3}{2}=-\frac{5\cdot3}{4\cdot2}=?\]

Answer 96

Wait, do you know what this means?

Answer 97

What exactly?

Answer 98

That im a complete and utter failure and that i will never become a physicist.