How do you solve 3/4 - 1/6x = 1/2 + 2x/9 for x?
- print Print
- list Cite
Expert Answers
calendarEducator since 2012
write511 answers
starTop subjects are Math, Science, and Business
Bring all terms in the variable `x` to one side of the equation and all the terms not in `x` to the other side. When a term switches sides it's sign switches. So if it is positive it becomes negative and if it is negative it becomes positive.
This gives
`-1/6x - 2/9x = 1/2 - 3/4`
Notice that the term `2/9x` switched sign from positive to negative as it was brought over to the left and the term `3/4` also switched sign from positive to negative as it was brought over to the right.
Now we gather the terms in `x` so that we have just one term:
`(-1/6 -2/9)x = 1/2 -3/4`
Now we combine the fractions
`(-3/18 - 4/18)x = 2/4 - 3/4`
Note 18 is the lowest common multiple of 6 and 9 ( = 3 x 6 and 2 x 9)
` `This gives
`-7/18x = -1/4`
To solve for ` ``x`multiply both sides by (-18/7). This gives
`x = (-1/4)(-18/7) = ((-1)(-18))/((4)(7)) = 18/28`
Simplifying this fraction (dividing both numerator and denominator by 2) we have
`x = 9/14` result (check on a calculator that both sides of the original equation = 0.643)
Related Questions
- Solve for x :- 1) x^(-3) + x^(-3/2) = 2 2) 6(4^x + 9^x) = 6^x(4+9)
- 1 Educator Answer
- How we simplify 2x/(x^2 -6x+9) - 1/(x+1) - 8/(x^2 -2x-3)
- 2 Educator Answers
- x^3+2x^2-x-2=0 solve for x
- 1 Educator Answer
- Solve for x (x^2-9)^1/2=4
- 1 Educator Answer
- Solve for x : 1/(x^2+6x+9) + 1/(x+3) = 4/9
- 1 Educator Answer
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.