How do you solve #10x + 2- 2x = 8( x + 1) - 7#?

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Answer 1 · 2016-12-23T19:07:44

#2 = 1#

Because we know #2# in fact does not equal one there is no solution to this problem for #x# other than the null set or #x = {O/}#

First expand the term in parenthesis on the right side of the equation:

#10x + 2 - 2x = (color(red)(8) * color(blue)(x)) + (color(red)(8) * color(blue)(1)) - 7#

#10x + 2 - 2x = 8x + 8 - 7#

Next, rearrange and combine like terms on each side of the equation:

#10x - 2x + 2 = 8x + 8 - 7#

#(10 - 2)x + 2 = 8x + 1#

#8x + 2 = 8x + 1#

Now subtract #8x# from each side of the equation to eliminate the variable and keep the equation balanced:

#8x - 8x + 2 = 8x - 8x + 1#

#0 + 2 = 0 + 1#

#2 = 1#

Because we know #2# in fact does not equal one there is no solution to this problem for #x# other than the null set or #x = {O/}#