How do you solve #-3p + 8= 6- ( 12p + 5)#?

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Answer 1 · 2017-04-01T19:09:43

See the entire solution process below:

First, remove the terms from parenthesis on the right side of the equation, group and combine like terms:

#-3p + 8 = 6 - (12p + 5)#

#-3p + 8 = 6 - 12p - 5#

#-3p + 8 = 6 - 5 - 12p#

#-3p + 8 = 1 - 12p#

Next, subtract #color(red)(8)# and add #color(blue)(12p)# to each side of the equation to isolate the #p# term while keeping the equation balanced:

#-3p + 8 - color(red)(8) + color(blue)(12p) = 1 - 12p - color(red)(8) + color(blue)(12p)#

#-3p + color(blue)(12p) + 8 - color(red)(8) = 1 - color(red)(8) - 12p + color(blue)(12p)#

#(-3 + color(blue)(12))p + 0 = -7 - 0#

#9p = -7#

Now, divide each side of the equation by #color(red)(9)# to solve for #p# while keeping the equation balanced:

#(9p)/color(red)(9) = -7/color(red)(9)#

#(color(red)(cancel(color(black)(9)))p)/cancel(color(red)(9)) = -7/9#

#p = -7/9#