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

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I usually do it in my head so I don't write it all out. Thank you for your help!In summary, the conversation discusses solving the equation 1/6(3/4x-2)=-1/5 by multiplying both sides by the least common multiple of 5 and 6, distributing the coefficient, and then isolating the variable x. The final solution is x = 16/15.
  • #1
OMGMathPLS
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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?
 
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  • #2
We are given:

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

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

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

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

Now, distribute the 5 on the left side...what do you get?
 
  • #3
$\frac{1}{6}(\frac{3}{4}x-2)=-\frac{1}{5}$

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

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

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

$x=\frac{16}{15}$
 
  • #4
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
 
  • #5
OMGMathPLS said:
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.
 
  • #6
OMGMathPLS said:
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:

\(\displaystyle \frac{15}{4}x-10=-6\)

So add $10$ to both sides, then multiply through by \(\displaystyle \frac{4}{15}\)...what do you get?
 
  • #7
you have 15/4x = 4

- - - Updated - - -

I don't know how you would isolate the x because it's really entangled in the ()
 
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  • #8
OMGMathPLS said:
you have 15/4x = 4

Correct, now multiply both sides by \(\displaystyle \frac{4}{15}\)...:D
 
  • #9
Oh ok.

15/4(4/15)x = 4

x = 4/1 * 15/4

so that's x =60/4
 
  • #10
OMGMathPLS said:
Oh ok.

15/4(4/15)x = 4

x = 4/1 * 15/4

so that's x =60/4

No, we have:

\(\displaystyle \frac{15}{4}x=4\)

Multiply through by \(\displaystyle \frac{4}{15}\):

\(\displaystyle \frac{\cancel{4}}{\cancel{15}}\cdot\frac{\cancel{15}}{\cancel{4}}x=\frac{4}{15}\cdot\frac{4}{1}\)

\(\displaystyle x=\frac{16}{15}\)
 
  • #11
ok. makes sense. thank you!

I guess it helps to write it out fully.
 

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

What is a fraction?

A fraction is a mathematical expression that represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number) separated by a horizontal line.

How do I add or subtract fractions?

To add or subtract fractions, you need to have a common denominator. If the denominators are different, you need to find the least common multiple (LCM) of the two denominators and convert the fractions into equivalent fractions with the LCM as the denominator. Then, you can simply add or subtract the numerators and keep the denominator the same.

Can fractions be simplified?

Yes, fractions can be simplified. To simplify a fraction, you need to find the greatest common factor (GCF) of the numerator and denominator and divide both by the GCF. The resulting fraction will have the smallest possible numerator and denominator.

How do I multiply or divide fractions?

To multiply fractions, you simply multiply the numerators and denominators. To divide fractions, you need to invert the second fraction (flip the numerator and denominator) and then multiply. It is also a good practice to simplify the resulting fraction if possible.

Can fractions be converted into decimals or percentages?

Yes, fractions can be converted into decimals or percentages. To convert a fraction into a decimal, divide the numerator by the denominator. To convert a fraction into a percentage, multiply the decimal equivalent by 100 and add a percentage sign.

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