How do you solve #7( a - 2) - 3= 4a - 5+ 3a#?

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Answer 1 · 2017-07-16T01:19:58

See a solution process below:

First, expand, group and combine like terms on each side of the equation:

#color(red)(7)(a - 2) - 3 = 4a - 5 + 3a#

#(color(red)(7) xx a) - (color(red)(7) xx 2) - 3 = 4a + 3a - 5#

#7a - 14 - 3 = (4 + 3)a - 5#

#7a - 17 = 7a - 5#

Next, subtract #color(red)(7a)# from each side of the equation:

#-color(red)(7a) + 7a - 17 = -color(red)(7a) + 7a - 5#

#0 - 17 = 0 - 5#

#-17 != -5#

Because #-17# does not equal #-5# this shows there is no solution to this equation. Or, the solution is the null or empty set: #{O/}#