How do you solve #\frac { 2x } { 5} - \frac { x + 18} { 6} = 23+ \frac { x } { 30}#?

Question

Kennedy Adams · Accepted Answer

#x = 130# Rearrange the equation. all #x#'s on one side. #(2x)/5 - (x + 18 )/6 -x/30 = 23# Equalize the denominators to #30# #(2x)/5 * 6/6 - (x + 18 )/6 * 5/5 -x/30 = 23# #(12x) / 30 - (5(x + 18)) / 30 - x/30 = 23# #( 12x -5x -90 -x ) / 30 =23# Multiply both sides by #30# #12x - 5x -90 -x = 690# #6x = 690 + 90# #6x = 780# #x = 780 / 6# #x =130#

Avery Alexander · Answer

#x = 130#

#(2x)/5 - (x+18)/6 = 23 + x/30#

You can eliminate fractions from an equation right away if it contains any of them.

After multiplying each term by the denominators' LCM, cancel.

In this case the LCM = #color(blue)(30#

#(color(blue)(30 xx)2x)/5 - (color(blue)(30 xx)(x+18))/6 = color(blue)(30 xx)23 + (color(blue)(30 xx)x)/30#

Currently, eliminate every denominator:

#(color(blue)(cancel30^6 xx)2x)/cancel5 - (color(blue)(cancel30^5 xx)(x+18))/cancel6 = color(blue)(30 xx)23 + (color(blue)(cancel30 xx)x)/cancel30#

#6 xx2x-5(x+18)= 30xx23 +x" "larr# no fractions!! Simplify

#12x-5x-90 = 690+x" "larr# now solve the equation

#12x-5x-x = 690+90" "larr# re-arrange the terms

#6x = 780" "larr div 6# on both sides

#x = 130#

Avery Alexander · Answer

undefined To solve the equation $\frac { 2x } { 5} - \frac { x + 18} { 6} = 23+ \frac { x } { 30}$, follow these steps:

1. Find a common denominator for all fractions.
2. Multiply each term by the common denominator to clear the fractions.
3. Simplify and solve for $x$.