How do you solve #\frac { x + 3} { 2} + \frac { 2x } { 7} = 7#?

1 Answer
Jun 20, 2018

Answer:

See a solution process below:

Explanation:

First, multiply each side of the equation by #color(red)(14)# to eliminate the fractions while keeping the equation balanced. #color(red)(14)# is the Least Common Denominator for the two fractions:

#color(red)(14)((x + 3)/2 + (2x)/7) = color(red)(14) xx 7#

#(color(red)(14) xx (x + 3)/2) + (color(red)(14) xx (2x)/7) = 98#

#(cancel(color(red)(14))7 xx (x + 3)/color(red)(cancel(color(black)(2)))) + (cancel(color(red)(14))2 xx (2x)/color(red)(cancel(color(black)(7)))) = 98#

#7(x + 3) + 4x = 98#

#(7 xx x) + (7 xx 3) + 4x = 98#

#7x + 21 + 4x = 98#

Next, we can group and combine like terms on the left side of the equation:

#7x + 4x + 21 = 98#

#(7 + 4)x + 21 = 98#

#11x + 21 = 98#

Then, subtract #color(red)(21)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#11x + 21 - color(red)(21) = 98 - color(red)(21)#

#11x + 0 = 77#

#11x = 77#

Now, divide each side of the equation by #color(red)(11)# to solve for #x# while keeping the equation balanced:

#(11x)/color(red)(11) = 77/color(red)(11)#

#(color(red)(cancel(color(black)(11)))x)/cancel(color(red)(11)) = 7#

#x = 7#