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5 votes
Solve for x. Express the answer in simplest form.
2/1= 8x-2/9

User Sebazzz
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2 Answers

3 votes
2/1= 8x-2/9
2= 8x-2/9
18=72x-2
20=72x
x=20/72
x= 5/18
User JonHendrix
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8.5k points
4 votes
First, you put known numbers apart ( numbers without x ) and unknown numbers apart (numbers with x ), and of course don't forget that when you move a number from a part to another, his sign change, So you get:

(2)/(1) = 8x - (2)/(9)

(2)/(1) + (2)/(9) = 8x

Now, you need to have the same denominator so you can add 2/1 and 2/9. So, you multiply 2/1 by 9, so you get:

(2*9)/(1*9) + (2)/(9) = 8x

(18)/(9) + (2)/(9) = 8x

Then you add the 2 fractions and you get:

(20)/(9) = 8x

Now, you divide each term by 8, so you get:

( (20)/(9) )/(8) = (8x)/(8)

in
(8x)/(8), you removed 8 and 8 and you get x, so you get:

( (20)/(9) )/(8) = x

as you know, 8 = 8/1, and when you got a division of 2 fractions, you multiply the first by the inverse of the second, which means you get:

(20)/(9) * (1)/(8) = x

And now you multiply, so you get:

(20*1)/(9*8)

(20)/(72)

20 and 72 have a common factor, so you divide each by 4, and you get:

(20/4)/(72/4)

(5)/(18)

So,
x = (5)/(18)

Hope this Helps! :D




User Rodd
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9.0k points