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

Question

Nathan Axel · Accepted Answer

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#

Ethan Adkins · Answer

undefined To solve the equation 6 = 3(r + 6) + 5(r + 4) using the distributive property, first distribute the terms inside the parentheses:

3(r + 6) = 3r + 18
5(r + 4) = 5r + 20

Now, substitute these expressions back into the original equation:

6 = 3r + 18 + 5r + 20

Combine like terms:

6 = 8r + 38

Subtract 38 from both sides:

6 - 38 = 8r
-32 = 8r

Divide both sides by 8:

-4 = r