How do you solve #5/9x+3=2/3#?

2 Answers
Feb 1, 2017

Answer:

See the entire solution process below:

Explanation:

First, multiply each side of the equation by #color(red)(9)# to eliminate the fraction while keeping the equation balanced. Eliminating the fraction will make the problem easier to work with.

#color(red)(9)(5/9x + 3) = color(red)(9) xx 2/3#

#(color(red)(9) xx 5/9x) + (color(red)(9) xx 3) = cancel(color(red)(9))3 xx 2/color(red)(cancel(color(black)(3)))#

#(cancel(color(red)(9)) xx 5/color(red)(cancel(color(black)(9)))x) + 27 = 6#

#5x + 27 = 6#

Next, subtract #color(red)(27)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#5x + 27 - color(red)(27) = 6 - color(red)(27)#

#5x + 0 = -21#

#5x = -21#

Now, divide each side of the equation by #color(red)(5)# to solve for #x# while keeping the equation balanced:

#(5x)/color(red)(5) = -21/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -21/5#

#x = -21/5#

Feb 1, 2017

Answer:

#x=-21/5#

Explanation:

A fraction consists of: #" "("count")/("size indicator") -> ("numerator")/("denominator")#

You can not directly subtract or add the counts (numerators) unless the size indicators (denominators) are the same.

#color(green)((5x)/9+[3color(red)(xx1)]=2/3color(red)(xx1)#

#color(green)((5x)/9+[3color(red)(xx9/9)]=2/3color(red)(xx3/3)#

#color(green)((5x)/9+[27/9]=6/9)#

As all the denominators (size indicators) are the same it is equally true that:

#5x+27=6#

Subtract 27 from both sides

#5x=-21#

Divide both sides by 5

#x=-21/5#