Question

Solve Each Equation.
1/x+1/2x=1/6

Answer 1

@Mertsj can you help here? This person isn't online... but I want to know if I am solving this right.

Answer 2

\[\frac{1}{x}+\frac{1}{2x}=\frac{2}{2x}+\frac{1}{2x}=\frac{3}{2x}\]

Answer 3

So we have the proportion:
\[\frac{3}{2x}=\frac{1}{6}\]

Answer 4

Cross multiply and solve.

Answer 5

Wait but... when you multiplied you multiplied by the 2 in the denominator though right?

Answer 6

\[\frac{1}{x}\times \frac{2}{2}=\frac{2}{2x}\]

Answer 7

So I replaced 1/x with 2/2x

Answer 8

Then since the denominators of the two fractions are the same, you can add them by adding the numerators.

Answer 9

\[2(\frac{ 1 }{ 2 }x) = x\]

Answer 10

Can I show you what I was trying to do?

Answer 11

That is true.

Answer 12

yes

Answer 13

\[2(\frac{ 1 }{ x } + \frac{ 1 }{ 2 }x = \frac{ 1 }{ 6 })\]

Answer 14

\[\frac{ 2 }{ x } + x = \frac{ 1 }{ 3 }\]

Answer 15

Right so far?

Answer 16

Could this work?

Answer 17

I am confused about what the original problem is

Answer 18

Is it this:
\[\frac{1}{x}+\frac{1}{2x}=\frac{1}{6}\]

Answer 19

or
\[\frac{1}{x}+\frac{1}{2}x=\frac{1}{6}\]

Answer 20

I believe so.

Answer 21

Oh, I mean the 2nd one

Answer 22

So what you have written is correct.

Answer 23

\[\frac{2}{x}+x=\frac{1}{3}\]

Answer 24

\[x(\frac{ 2 }{ x } + x = \frac{ 1 }{ 3 })\]

Answer 25

yes

Answer 26

\[2+x ^{2}=\frac{ 1 }{ 3 }x\]

Answer 27

yes

Answer 28

Now I am stuck...

Answer 29

because I have x^2...

Answer 30

Multiply both sides by 3

Answer 31

\[6 + 3x ^{2} = x\]

Answer 32

yes. Now subtract x from both sides.

Answer 33

\[3x ^{2}-x+6\]

Answer 34

set equal to 0

Answer 35

=0

Answer 36

Now use the quadratic formula because I don't think it will factor.

Answer 37

ok

Answer 38

\[\frac{ 1\pm {71i} }{ 6 }\]

Answer 39

?

Answer 40

sqrt71

Answer 41

\[\frac{ 1\pm \sqrt{-71} }{ 6 }\]

Answer 42

but we can't have a negative under the radical because it is imaginary right?

Answer 43

\[\frac{1\pm \sqrt{71}i}{6}\]

Answer 44

Oh, haha... thank you :)

Answer 45

yw. But it might have been easier to clear all the fractions right at the beginning by multiplying by the common denominator which is 6x

Answer 46

\[6x \times\frac{1}{x}\times+6x \times \frac{1}{2}x=6\times\frac{1}{6}\]

Answer 47

\[6+3x^2=x\]

Answer 48

\[3x^2-x+6=0\]

Answer 49

oh I see

Answer 50

Good.