How do you solve #\frac { 2( x + 5) } { 4} = 5x - 2#?

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Answer 1 · 2017-01-28T19:56:03

See the entire solution process below:

First, multiply each side of the equation by #color(red)(4)# to eliminate the fraction while keeping the equation balanced:

#color(red)(4) xx (2(x + 5))/4 = color(red)(4)(5x - 2)#

#cancel(color(red)(4)) xx (2(x + 5))/color(red)(cancel(color(black)(4))) = 20x - 8#

#2(x + 5) = 20x - 8#

Next, expand the terms in parenthesis on the left side of the equation:

#2x + 10 = 20x - 8#

Then, subtract #color(red)(2x)# and add #color(blue)(8)# to each side of the equation to isolate the #x# term:

#2x + 10 - color(red)(2x) + color(blue)(8) = 20x - 8 - color(red)(2x) + color(blue)(8)#

#2x - color(red)(2x) + 10 + color(blue)(8) = 20x - color(red)(2x) - 8 + color(blue)(8)#

#0 + 18 = 18x - 0#

#18 = 18x#

Now, divide each side of the equation by #color(red)(18)# to solve for #x# while keeping the equation balanced:

#18/color(red)(18) = (18x)/color(red)(18)#

#1 = (color(red)(cancel(color(black)(18)))x)/cancel(color(red)(18))#

#1 = x#

#x = 1#