Answer:
-1 1/6
Step-by-step explanation:
Use a common denominator first to convert all the fractions so they can be easily added or subtracted.
Common denominator is 18 since 3, 6, and 9 can all evenly divide into 18
1/3 = 6/18
1/6 = 3/18
2/9 = 4/18
So now you have
-6/18x - 3/18 = 4/18
add 6/18x to both sides so you can make the number with the variable positive
6/18x - 6/18x - 3/18 = 4/18 + 6/18x simplifies to - 3/18 = 4/18 + 6/18x
subtract 4/18 from both sides
- 3/18 - 4/18 = 4/18 - 4/18 + 6/18x simplifies to - 7/18 = 6/18x
Divide both sides by 6/18 so x is alone on the one side
( - 7/18) / ( 6/18) = ( 6/18x) / ( 6/18) simplifies to ( - 7/18) / ( 6/18) = x
When you divide a fraction by a fraction, the bottom fraction gets flipped over then you multiply the two new fractions straight across
so the new equation looks like this
- 7/18 times 18/6 and you multiply -7 x 18 = -126 and the bottom is 18 times 6 = 108 you now have -126/108
x = -126/108 which simplifies to - 1 18/108 which can still be simplified more to -1 1 / 6 since 108 can be divided by 18 that gives you 6.
