Question

How do you solve: \[\frac{7-5x}{4}=-2\]

Answer 1

multiply both sides by 4, you get
7-5x=-8
7+8=5x
15=5x
x=15/3
x=3

Answer 2

* x=15/5

Answer 3

I'm sorry, but that makes no sense. I don't know how to get the 7 down from the \[\frac{7-5x}{4}\] if i could do that, then i know how to solve the problem.

Answer 4

\[\frac{ 7-5x }{ 4 } 4 = 7-5x\]

Answer 5

Wheres the reciprocal then?

Answer 6

because you can't do \[\frac{4}{7-5x}\] with out messing up the equation, and you can't just multiply them by 4.

Answer 7

you can multiply both sides of equation by the same number and you won't change the result. So, multiply fraction by 4 and multiply -2 by 4 and you will get what I wrote above.

Answer 8

But that's not right. If you had a problem like: \[\frac{9}{4}k=-36\] you would do this: \[(\frac{4}{9})(\frac{9}{4})k=-36(\frac{4}{9})\] then you would divide -36 by 9, to get four, then four times four. How would you do that to this problem?

Answer 9

if you multiply
\[\frac{ 9 }{ 4 }k=-36\] by 4, you'll get
9k=-36*4
then you divide this equation by 9 and you get
k=-\[k=-\frac{ 36 }{ 9 } 4\]
k=-4*4
k=-16
You will get the same result if you multiply equation from the start by 4/9. Right?

Ok, if you want reciprocal for your first question, you can write 4 as \[\frac{ 4 }{ 1 }\]. Ok?

Answer 10

But that's not the reciprocal! The reciprocal of the problem would cancel them out, and I can't do it like that!

Answer 11

ok, tell me, what is reciprocal for \[\frac{ 1 }{ 4 }\]?

Answer 12

The reciprocal for \[\frac{1}{4}\] is \[\frac{4}{1}\] but the reciprocal for \[\frac{7-5x}{4}\] isn't 4, its \[\frac{4}{7-5x} which would cancel out the x, and just leave you with a normal number.

Answer 13

you can't cancel out x because you have to find a value of x

Answer 14

that's the aim, to find value of x.

Answer 15

That's what i'm saying!

Answer 16

Do you know that \[\frac{ a }{ b }=\frac{ c }{ d }\] is the same as a*d=c*b ?

Answer 17

Yes i do, But you're seriously confusing me.

Answer 18

Ok, good! Then let me help you.

Answer 19

Then make it easily understandable!

Answer 20

\[\frac{ 7-5x }{ 4 }=-2\] is the same as
\[\frac{ 7-5x }{ 4 }=\frac{ -2 }{ 1 }\] because \[-2=\frac{ -2 }{ 1 }\]

now you have, from
\[\frac{ a }{ b }=\frac{ c }{ d } <=> a*d=c*b\],
(7-5x)*1=4*(-2)
7-5x=-8
7+8=5x
15=5x
x=3

Answer 21

ok?

Answer 22

you misunderstand the "multiply by the reciprocal" rule

in your problem
\[ \frac{1}{4} \cdot (7-5x) = -2\]

one way to solve is to multiply both sides by 4
\[ \frac{4}{4} \cdot (7-5x) = -2\cdot 4\]

Answer 23

That's not my problem though, my problem is this: \[\frac{7-5x}{4}\] that's what it is.

Answer 24

as you know,
\[ \frac{7-5x}{4} = \frac{1}{4} \cdot (7-5x) \]

Answer 25

I'm giving up :D

Answer 26

another way to write it is
\[ \frac{7-5x}{4} = \frac{7}{4} - \frac{5x}{4} \]

Answer 27

dividing by 4 is the same as multiplying by 1/4

Answer 28

I don't get it.

Answer 29

which part ?

Answer 30

The reciprocal part. How do you get 1/4??

Answer 31

maybe it makes more sense if we use numbers as examples:
Example:
\[ \frac{8}{4}=2 \\ \text{ and } \\
\frac{1}{4} \cdot 8= 2\]

dividing 8 by 4 is the same as multiplying 8 by 1/4

Answer 32

So how do you get 1/4 from 7-5x/4? that's what i need to know...

Answer 33

if you know how to multiply fractions (top times top over bottom times bottom) we can say
\[ \frac{1}{4} \cdot 8 = \frac{1}{4} \cdot\frac{8}{1}=\frac{1 \cdot 8}{4 \cdot 1}= \frac{8}{4} = 2 \]

Answer 34

that same rule works for complicated expressions like 7-5x (instead of 8)

Answer 35

OKay, but still, how do you separate the 7/4 from the -5x/4?

Answer 36

Here is an example of how to add two fractions with the same denominator,
\[ \frac{ 1}{4} + \frac{3}{4} \]
the answer is : keep the same denominator and add the numerators
\[ \frac{ 1}{4} + \frac{3}{4}= \frac{1+3}{4}\]
notice you can switch between those two forms

example
\[ \frac{7-5x}{4} = \frac{7}{4} + \frac{-5x}{4} \]

Answer 37

another way to solve your problem (though this is a bit messy)
\[ \frac{7}{4} + \frac{-5x}{4}= -2 \\ \frac{-5x}{4}= -2-\frac{7}{4} \]
simplify, then multiply both sides by -4/5

Answer 38

okay, i'm beyond confused. >.< i just need to answer these last few questions...

Answer 39

can you solve for x in
\[ \frac{4}{4} \cdot (7-5x) = -2\cdot 4 \]?

Answer 40

4/4 is 1
-2*4 is -8
so you get
\[ 7 -5x= -8\]
can you finish ?

Answer 41

\[7-5x=-8\]\[-7=-7\]\[-5x=15\]\[\frac{-5x}{5}=\frac{-15}{-5}\]\[x=3\] right?

Answer 42

yes, though you have a typo on the 2nd to last line: you mean -5x/ -5

but that is the answer.

Now to do the original problem you have to convince your self that multiplying both sides by 4 is a good thing to do.

Answer 43

Okay, but still, how would you get the four from \[\frac{7-5x}{4} That's what i don't understand.

Answer 44

Can you answer this
\[ 4 \cdot \frac{x}{4} = \]?

Answer 45

no. not correctly at least.

Answer 46

can you do
\[ 4 \cdot \frac{2}{4} \]?

Answer 47

uhh. would it be: \[\frac{8}{16}\] or \[\frac{1}{2}\]?

Answer 48

a calculator would tell you. But if you don't understand fractions you will get stuck doing algebra.
when you get time, see
http://www.khanacademy.org/math/arithmetic/fractions/multiplying_and_dividing_frac/v/multiplying-fractions
(and any of the videos about fractions that you don't know)


but the rule for multiplying fractions is multiply top times top and bottom times bottom
if one of the numbers is a whole number, set its "bottom" to 1

\[ 4 \cdot \frac{2}{4}= \frac{4}{1}\cdot \frac{2}{4} = \frac{4\cdot 2}{1\cdot 4}\]

Answer 49

one of the rules you know about multiplying is you can swap the order. so
\[ \frac{4\cdot 2}{1\cdot 4} = \frac{2\cdot 4}{1\cdot 4}\]
we can think of that as multiplying
\[ \frac{2}{1}\cdot \frac{4}{4}\]
of course 4/4 is 1
\[ \frac{2}{1}\cdot 1 \]
and that simplifies to 2

if you practice, you will learn that if you have the same thing in the top and bottom (like the 4 in this example), you can cancel it. and get 2 immediately

Answer 50

so if you see
\[ 4 \cdot \frac{2}{4}= \cancel{4} \cdot \frac{2}{\cancel{4}} =2 \]

Answer 51

\[ \frac{7-5x}{4} = -2 \\ 4 \cdot \frac{7-5x}{4} = -2 \cdot 4 \]

now use the rule "cancel" the 4, because you have a 4 in the top and bottom