How do you solve #3.5- 9a = 2( 0.5a - 4)#?

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Answer 1 · 2017-07-03T16:37:55

See a solution process below:

First, expand the terms on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

#3.5 - 9a = color(red)(2)(0.5a - 4)#

#3.5 - 9a = (color(red)(2) xx 0.5a) - (color(red)(2) xx 4)#

#3.5 - 9a = 1a - 8#

Next, add #color(red)(9a)# and #color(blue)(8)# to each side of the equation to isolate the #a# term while keeping the equation balanced:

#3.5 - 9a + color(red)(9a) + color(blue)(8) = 1a - 8 + color(red)(9a) + color(blue)(8)#

#3.5 + color(blue)(8) - 9a + color(red)(9a) = 1a + color(red)(9a) - 8 + color(blue)(8)#

#11.5 - 0 = (1 + color(red)(9))a - 0#

#11.5 = 10a#

Now, divide each side of the equation by #color(red)(10)# to solve for #a# while keeping the equation balanced:

#11.5/color(red)(10) = (10a)/color(red)(10)#

#1.15 = (color(red)(cancel(color(black)(10)))a)/cancel(color(red)(10))#

#1.15 = a#

#a = 1.15#