MHB Fraction Question: How to Solve 1/6(3/4x-2)=-1/5?

[OMGMathPLS]

1/6(3/4x-2)=-1/5

The answer is 16/15

So to get that you multiply by reciprocal, right?

So you take the -1/5 and make it a 1 by fliping it over to -5/1.

Then you do to the other side the -5/1 and so that's -5/6(3/4x-2)=1

and then there's a -2 so you +2 it and do it to the other side so that's

-5/6(3/4x)=3

And then do you multiply the fractions by flipping one or do you move the x?

 

[MarkFL]

We are given:

$$\frac{1}{6}\left(\frac{3}{4}x-2\right)=-\frac{1}{5}$$

The first thing I would do here is multiply by LCM(5,6) = 30 to get rid of the denominators of 5 and 6:

$$30\cdot\frac{1}{6}\left(\frac{3}{4}x-2\right)=30\left(-\frac{1}{5}\right)$$

$$5\left(\frac{3}{4}x-2\right)=-6$$

Now, distribute the 5 on the left side...what do you get?

 

[ineedhelpnow]

$\frac{1}{6}(\frac{3}{4}x-2)=-\frac{1}{5}$

$\frac{3}{4}x-2=-\frac{1}{5}*6$ (you flip the 1/6 and multiply)

$\frac{3}{4}x-2=-\frac{6}{5}$

$\frac{3}{4}x=-\frac{6}{5}+\frac{10}{5}$ (10/5 is equal to 2 you just want common denominators so you can easily add)

$\frac{3}{4}x=\frac{4}{5}$

$x=\frac{4}{5}* \frac{4}{3}$

$x=\frac{16}{15}$

 

[OMGMathPLS]

If you distribute it on the left side

you get

5/1 (3/4x-2)

so you just multiply the fractions across

15/4 and -10/1 so -10

so it's 15/4x and -10

 

[ineedhelpnow]

1/6(3/4x-2)=-1/5

The answer is 16/15

So to get that you multiply by reciprocal, right?

So you take the -1/5 and make it a 1 by fliping it over to -5/1.

Then you do to the other side the -5/1 and so that's -5/6(3/4x-2)=1

and then there's a -2 so you +2 it and do it to the other side so that's

-5/6(3/4x)=3

And then do you multiply the fractions by flipping one or do you move the x?

you cannot just pull out the -2 from the parenthesis and add it to the other side. you would first have to distribute the -5/6. what you want to do is isolate the x to solve for so try moving this from the left side of the equation (where the x is) to the other side.

 

[MarkFL]

If you distribute it on the left side

you get

5/1 (3/4x-2)

so you just multiply the fractions across

15/4 and -10/1 so -10

so it's 15/4x and -10

Correct, so you have:

$$\frac{15}{4}x-10=-6$$

So add $10$ to both sides, then multiply through by $$\frac{4}{15}$$...what do you get?

 

[OMGMathPLS]

you have 15/4x = 4

- - - Updated - - -

I don't know how you would isolate the x because it's really entangled in the ()

 

[MarkFL]

you have 15/4x = 4

Correct, now multiply both sides by $$\frac{4}{15}$$...:D

 

[OMGMathPLS]

Oh ok.

15/4(4/15)x = 4

x = 4/1 * 15/4

so that's x =60/4

 

[MarkFL]

Oh ok.

15/4(4/15)x = 4

x = 4/1 * 15/4

so that's x =60/4

No, we have:

$$\frac{15}{4}x=4$$

Multiply through by $$\frac{4}{15}$$:

$$\frac{\cancel{4}}{\cancel{15}}\cdot\frac{\cancel{15}}{\cancel{4}}x=\frac{4}{15}\cdot\frac{4}{1}$$

$$x=\frac{16}{15}$$

 

[OMGMathPLS]

ok. makes sense. thank you!

I guess it helps to write it out fully.