How do you solve #6( x + 1/ 2) = 3x + 3+ 3x#?

1 Answer
smendyka
May 30, 2017

See a solution process below:

Explanation:

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

#color(red)(6)(x + 1/2) = 3x + 3 + 3x#

#(color(red)(6) xx x) + (color(red)(6) xx 1/2) = 3x + 3 + 3x#

#6x + 3 = 3x + 3 + 3x#

Now, group and combine like terms on the right side of the equation:

#6x + 3 = 3x + 3x + 3#

#6x + 3 = (3 + 3)x + 3#

#6x + 3 = 6x + 3#

Because both sides of the equation are exactly the same we know for any and all values of #x# this equation will be true. Therefore, the solution is the set of all real numbers or #{RR}#

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