Question

(x+4)/6 = 5/6 - (x-1)/4

Please help. I worked this out already but got it wrong.

Answer 1

hope that help @katiexo

Answer 2

still lost. thought I had to find the LCD first and get a common denominator

Answer 3

yea nvm i make it easy

Answer 4

i know the lcd is 12

Answer 5

x+46=56−x−14 ok so Step-By-Step Solution:
Multiply both sides of the equation by 6.
(x+4)=(56−x−14)⋅(6)

Answer 6

Indeed, finding the lowest common denominator and then using it to eliminate the fractions is the way to go. I agree that 12 is the LCD. Good.

What next?

Why not copy the problem, as given, and then mult. each term by the LCD? Simplify the result. Good-bye, fractions.

Answer 7

I get to 10 - 3x - 3 = 2x + 8, but when I simplify further I get the wrong answer.

Answer 8

@mathmale

Answer 9

(x+4)/6 = 5/6 - (x-1)/4
(x+4)/6 = 5/6 + (-x+1)/4
(x+4) = 5 + (- 6x + 6)/4 (multiplied both sides by 6)
4x + 16 = 5 - 6x +6 (multiplied both sides by 4)
4x + 16 = -6x +11 (simplified 5+6)
can you simplify that?

Answer 10

Indeed, finding the lowest common denominator and then using it to eliminate the fractions is the way to go. I agree that 12 is the LCD. Good.

What next?

Why not copy the problem, as given, and then mult. each term by the LCD? Simplify the result. Good-bye, fractions.

Could we please come to agreement? Is the LCD 6 or is it 12?

Answer 11

It's 12, that's why I multiplied the terms by 12

Answer 12

Great. And your results?

Answer 13

Then I worked it out and got \[\frac{ 10 }{ 12 } - \frac{ 3x-3 }{ 12 } -\frac{ 2x+8 }{ 12 } = 0\]

Answer 14

then I double checked my answer

Answer 15

My answer key has the correct answer as simply 1

Answer 16

but it isnt...

Answer 17

This is the original equation (Ignore the '3')

Answer 18

Ah, a little friendly competition! Katie: Now that you have the same denom.., cancel out that den. What's left of your equation? Please show all the steps you go through to find the value of x that satisfies this equation.

Answer 19

how would 1 work?

Answer 20

So after that I just set the numerators equal to each other because they have the same denominator. So I was left with \[10-3x-3-2x+8 = 0\]

Answer 21

@RhondaSommer where are you getting that equation from? that's not the original equation. check my picture attachment

Answer 22

And? Combine like terms and solve for x.

Answer 23

Remember, you'll have to check your own answer by substitution.

Answer 24

lol I simply got myself confused...mathmale is right XD

Answer 25

Then I got \[15-5x = 0\]

Answer 26

so sorry XD

Answer 27

Then ended with x = 3 but that's not the answer in my answer key :/

Answer 28

I'm just so confused!

Answer 29

I plugged it back in and it's not right either. No idea where I'm going wrong...

Answer 30

Relax. You've demonstrated that you know what "Lcd" means and that you know how to find it. You do have an arithmetic error that we can fix.

Answer 31

I can't find my error

Answer 32

Your original problem:

screenshot20160207at6.08.30pm.png

Answer 33

Could you post it yoursxelf, katie?

Answer 34

You've stated, correctly, that the LCD is 12. Mult. the first fraction of your original eq'n by 12 and simplify the result.

Answer 35

Yes. It's \[\frac{ 5 }{ 6 } - \frac{ x-1 }{ 4 } = \frac{ x+4 }{ 6 }\]

Answer 36

Mult the first term by 12 and simplify the result as much as possible. What do you get?

Answer 37

Hint: 12/6 = 2, and 2*5+?

Answer 38

xxxx and 2*5=??

Answer 39

10/12 which reduces to 5/6?

Answer 40

Katie, we found the LCD and need to use it to eliminate fractions. So, no, we don't want that 5/6. 2*5=?

Answer 41

10

Answer 42

Yes. Now mult the 2nd term by 12 and reduce the result. Result?

Answer 43

\[\frac{ 3x-3 }{ 12 } ?\]

Answer 44

Why the 12 in the denom.? Again, our purpose was to eliminate fractions. That has not happened yet.

Answer 45

Because I was trying to get all the denoms the same first

Answer 46

So just 3x-3?

Answer 47

The 2nd term is -(x-1)/4. Mult that by 12 and cancel the 4.

You'd be correct if you'd please enclose that 3x-3 in parentheses and put a neg. sign in front of it. Try again.

Answer 48

The 2nd term is -(x-1)/4. Mult that by 12 and cancel the 4.

Answer 49

-(3x-3)?

Answer 50

Remember: the purpose of the LCD is to enable us to combine fractions.

Answer 51

In this particular case we also wanted to eliminate fractions.

Mult the 3rd term by 12 and simplify the result, please.

Answer 52

(2x+8)

Answer 53

Your -(3x-3) is fine, by the way.

Good. Now reconstruct the equation with NO denominator.

Answer 54

10 - ?? = ??

Answer 55

10 - (3x-3) = (2x+8)

Answer 56

Great. Now, carefully, eliminate the parentheses.

Answer 57

10 - 3x+3 = 2x+8

Answer 58

Combine like terms. The 2x on the right is already positive, so leave it there and move the 3x term.

Answer 59

13 = 5x + 8

Answer 60

subtract 8 from both sides and siimplify the equation.

Answer 61

x = 1!!!!

Answer 62

Oh my gosh finally!!! I see my only problem was that -(3x-3).

Answer 63

Now, go back to the original equation. Subst. 1 for x. Is the equation now true?

Answer 64

Yes! It'd be 5/6 = 5/6 - 0, so they're equal

Answer 65

Therefore, your x=1 is the correct solution. Congrats.

Answer 66

Thanks for all your help! :)

Answer 67

Mygreat pleasure, Katie. See you!