Question

1/8-x=3/5 i dont get how to solve this

Answer 1

you can solve equations by applying the same operation on both sides
this is ALWAYS possible in EVERY equation

Answer 2

you want x seperately, right? (the description for the unknown)

Answer 3

but what operation?

Answer 4

you can pick any operation, such as: addition of some number or constant, subtraction of some number or constant, multiplication of some number or constant, division of some number or constant.

of course, one wants to make operations that help - however, any operation is allowed AS LONG AS it is applied to BOTH SIDES

Answer 5

and yes about the x

Answer 6

\[\frac{ 3 }{ 5 } - \frac{ 1 }{ 8 } = x \]

Answer 7

yes we want the x separately. what is still bothering us?

Answer 8

1/8-x=3/5

Answer 9

i just dont get how to solve it can u give a example

Answer 10

yes

Answer 11

so we have this:

1/8-x=3/5

Answer 12

yes

Answer 13

two things are wrong:

1. there are numbers on the side of x....
2. the x is negative

Answer 14

okay

Answer 15

just take the -x to the opposite side and you will have an x,

Answer 16

the number is a positive fraction: 1/8

1/8-x=3/5

the following operation is allowed: subtracting a number
we choose as number 1/8

this is what we do:

1/8-x -1/8=3/5 -1/8

Answer 17

okay

Answer 18

-1/8 was introduced to both sides. this is okay as long as we introduce the same amount, the same sign -- on both sides!

Answer 19

then, if we calculate that we get:

1/8-x -1/8=3/5 -1/8
gives
-x = 3/5 - 1/8

Answer 20

okay

Answer 21

now the only issue is that x is still negative - that was problem 2)

Answer 22

to counter this problem, we can "MULTIPLY BY -1".
all it does is change the signs of every term when we multiply with -1
it doesn't change the values...

Answer 23

ok, so operation two: multiply by -1

before, we had:
-x = 3/5 - 1/8
now, we have:
x = -3/5 + 1/8

Answer 24

but why -1

Answer 25

because the x was negative:

-x = 3/5 - 1/8

Answer 26

we don't want -x = ...

we want x = ,,,

Answer 27

and MULTIPLICATION with -1 just changes the sign

3 * -1 = -3

:)

Answer 28

oh

Answer 29

you could have made other steps, as well

Answer 30

do you want to see a second way to solve this (without -1) ?

Answer 31

yes please

Answer 32

ok

original equation:
1/8-x=3/5

Answer 33

yes

Answer 34

now we can add x to both sides (Operation: addition of variable)

1/8-x+x=3/5 + x

-x + x = 0, so it is the same as:

1/8=3/5 + x

Answer 35

with this we were able to also get a positive x :)

Answer 36

then
1/8=3/5 + x

the 3/5 just needs to be subtracted away so x is alone

Answer 37

okay

Answer 38

\[\frac{ 1 }{ 8 } - x = \frac{ 3 }{ 5 }\]
\[\frac{ 1 }{ 8 } = x + \frac{ 3 }{ 5 }\]
\[-\frac{ 3 }{ 5 } + \frac{ 1 }{ 8 } = x\]

Answer 39

before:
1/8=3/5 + x

subtraction of 3/5 from both sides:

1/8 - 3/5 = x

Answer 40

last part again:

1/8 -3/5 =3/5 + x - 3/5

1/8 -3/5 = 3/5 - 3/5 + x

1/8 -3/5 = 0 + x
1/8 - 3/5 = x

Answer 41

I chose to subtract 3/5 because it cancels the 3/5 on the x side
that's why I subtract exactly that

Answer 42

okay so then you would find a common denominator and that would be 40

Answer 43

true

Answer 44

okay so it would be 5/40 - 24/40

Answer 45

yes

Answer 46

-19/40 ?

Answer 47

yes

Answer 48

yeah

Answer 49

that's the value of the uknown x
in simple form

Answer 50

oh ok

Answer 51

the same value was already in the original equation, we just couldn't see it ;)

Answer 52

because everything was over the place and split up, on the wrong side...

Answer 53

all information was already there

Answer 54

remember with this equation you can verify your answer, if you unsure. substitute x = (your answer) and see if LHS = RHS .

Answer 55

yes that's a good tip from @LinuxMint

Answer 56

1 more question 3/4-5/2x=1/3

Answer 57

we want x alone, there's a fraction that shouldn't be there: 3/4

Answer 58

OK so:

if there is a negative x, it is a good idea to add x to both sides

Answer 59

ok?

Answer 60

that's a new rule

Answer 61

k

Answer 62

ok, so we can add one x, or three x to both sides

Answer 63

however
it only makes sense to add the same amount that we have in negative

3/4-5/2x=1/3

Answer 64

what is the amount of negative x here?

Answer 65

k

Answer 66

do you know what coefficient of a variable is?

Answer 67

no

Answer 68

oh

Answer 69

well it is the number that's with the variable

3x

the 3 in this case

Answer 70

to solve equations with a NEGATIVE x, you must determine
this number

in front of x

Answer 71

3/4-5/2x=1/3

Answer 72

i think i got this now if i have any mor e ?s i will let you know

Answer 73

ok :)

Answer 74

in other terms, if there's -5/2 x
then you have to add 5/2 x to both sides,

if there's -3x
you have to add 3x to both sides,

if there's a -2/7 x
you have to add 2/7 x to both sides.

Answer 75

the -2/7 x will disappear on one side and appear positive on the other

Answer 76

that's how to deal with negative x's