How do you solve #\frac { 9} { 6} x + \frac { 5} { 3} = 4#?

2 Answers
Sep 19, 2017

#x=14/9#

Explanation:

The end goal is to solve for #x#, so we need to isolate the #x#.

Start by subtracting #5/3# on both sides, but to do that, we need to have common denominators, which in this case are #12#. So you need to change the fractions (still keeping the ratio) until the denominators are equal):

#9/6x+20/12=48/12#

Now you can subtract #20/12# from both sides:

#9/6x=28/12#

Multiply both sides by #6/9#:

#x=168/108#

Simplify:

#x=14/9#

Sep 23, 2017

#x=14/9#

Explanation:

If you are solving an equation which has fractions, you can get rid of them immediately by multiplying each term by the #LCD# (which is #color(blue)(6)# in this case.)

#9/6x +5/3 =4#

#(color(blue)(cancel6xx)9)/cancel6x +(color(blue)(cancel6^2xx)5)/cancel3 =color(blue)(6xx)4#

#9x +10 = 24" "larr# now solve as usual

#9x = 24-10#

#9x = 14#

#x = 14/9#

Note: A better approach would have been to simplify the first fraction to #3/2#, but the method and result is the same