How do you solve # 7/(9x)+2/3=5+1/(3x)#?

2 Answers
Jun 21, 2017

Answer:

#x=4/39#

Explanation:

to clear the denominators, multiply both sides by #9x#

#(9x)(7/(9x)) = 7#;
#(9x)(2/3) = 6x#;
#(9x)(5) = 45x#;
#(9x)(1/(3x))=3#

you now have #7+6x=45x+3#

by subtracting #6x# and 3 from both sides, you get #39x=4#

divide both sides by 39

#x=4/39#

Jun 22, 2017

Answer:

Multiply the equation by numbers that will eliminate the denominator terms.

Explanation:

In this case we would multiply the whole thing by 9x because that is the least value that includes factors from all of the denominators (x, 3, 9).
#(9*x)*(7/(9*x) + 2/3 = 5 + 1/(3*x))#

#7 + 6*x = 45*x + 3# ; Now we can solve for ‘x’ normally.

#4 = 39*x# ; #x = 0.103#

CHECK:
#7/(9*0.103) + 2/3 = 5 + 1/(3*0.103)#
#7/0.927 + 2/3 = 5 + 1/0.309#

#7.55 + 0.667 = 5 + 3.24#
#8.22 = 8.24# OK, given rounding errors.