How do you solve #x- 30+ 3x - 75+ \frac { 1} { 2} x + 15= 180#?

1 Answer
May 17, 2018

See a solution process below:

Explanation:

First, group and combine the like terms on the left side of the equation.

#x + 3x + 1/2x - 30 - 75 + 15 = 180#

#1x + 3x + 1/2x - 30 - 75 + 15 = 180#

#(1 + 3 + 1/2)x + (-30 - 75 + 15) = 180#

#(4 + 1/2)x + (-105 + 15) = 180#

#([2/2 xx 4] + 1/2)x + (-90) = 180#

#(8/2 + 1/2)x - 90 = 180#

#(8 + 1)/2x - 90 = 180#

#9/2x - 90 = 180#

Next, add #color(red)(90)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#9/2x - 90 + color(red)(90) = 180 + color(red)(90)#

#9/2x - 0 = 270#

#9/2x = 270#

Now, multiply each side of the equation by #color(red)(2)/color(blue)(9)# to solve for #x# while keeping the equation balanced:

#color(red)(2)/color(blue)(9) xx 9/2x = color(red)(2)/color(blue)(9) xx 270#

#cancel(color(red)(2))/cancel(color(blue)(9)) xx color(blue)(cancel(color(black)(9)))/color(red)(cancel(color(black)(2)))x = 540/9#

#x = 60#