How do you solve #6=3(r+6)+5(r+4)# using the distributive property?

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Answer 1 · 2017-02-06T23:19:47

See the entire solution process below:

First, expand the terms in parenthesis on the right side of the equation:

#6 = (3 xx r) + (3 xx 6) + (5 xx r) + (5 xx 4)#

#6 = 3r + 18 + 5r + 20#

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

#6 = 3r + 5r + 18 + 20#

#6 = (3 + 5)r + 38#

#6 = 8r + 38#

Next, subtract #color(red)(38)# from each side of the equation to isolate the #r# term while keeping the equation balanced:

#6 - color(red)(38) = 8r + 38 - color(red)(38)#

#-32 = 8r + 0#

#-32 = 8r#

Now, divide each side of the equation by #color(red)(8)# to solve for #r# while keeping the equation balanced:

#(-32)/color(red)(8) = (8r)/color(red)(8)#

#-4 = (color(red)(cancel(color(black)(8)))r)/cancel(color(red)(8))#

#-4 = r#

#r = -4#