How do you solve: #n + 2 = -14 - n#?

4 Answers
Apr 4, 2017

See the entire solution process below:

Explanation:

First, subtract #color(red)(2)# and add #color(blue)(n)# to each side of the equation to isolate the #n# term while keeping the equation balanced:

#n + 2 - color(red)(2) + color(blue)(n) = -14 - n - color(red)(2) + color(blue)(n)#

#n + color(blue)(n) + 2 - color(red)(2) = -14 - color(red)(2) - n + color(blue)(n)#

#1n + 1color(blue)(n) + 0 = -16 - 0#

#2n = -16#

Now, divide each side of the equation by #color(red)(2)# to solve for #n# while keeping the equation balanced:

#(2n)/color(red)(2) = -16/color(red)(2)#

#(color(red)(cancel(color(black)(2)))n)/cancel(color(red)(2)) = -8#

#n = -8#

Apr 4, 2017

#n=-8#

Explanation:

To solve this equation, collect terms in n on the left side and numeric values on the right side.

add n to both sides.

#n+n+2=-14cancel(-n)cancel(+n)#

#rArr2n+2=-14#

subtract 2 from both sides.

#2ncancel(+2)cancel(-2)=-14-2#

#rArr2n=-16#

divide both sides by 2

#(cancel(2) n)/cancel(2)=(-16)/2#

#rArrn=-8#

#color(blue)"As a check"#

Substitute this value into the equation and if the left side equals the right side then it is the solution.

#"left side " =-8+2=-6#

#"right side " =-14-(-8)=-14+8=-6#

#rArrn=-8" is the solution"#

Apr 4, 2017

#n =-8#

Explanation:

You need to get all the variables (#n#) on one side and all the numbers on the other.
You want to get to the answer: #n = "a value"#

In an equation, you have to do the SAME to BOTH sides, otherwise the sides will no longer be equal.

#n+2 =-14-n" "larr# add #n# to each side first

#n+2color(red)(+n) =-14-n color(red)(+n)#

#2n +2 = -14" "larr# subtract #2# from from sides

#2n +2 color(blue)(-2)= -14 color(blue)(-2)#

#2n = -16" "larr div 2# to isolate #n#

#(2n)/2 = (-16)/2#

#n =-8#

Note that #-n color(red)(+n) =0" " and " " +2 color(blue)(-2)=0#

Apr 4, 2017

#n="-"8#

Explanation:

First add #n# to both sides to eliminate it from the right side
#n+2color(green)(+n)="-"14color(red)(cancelcolor(black)(-n)cancelcolor(green)(+n))#
#2n+2="-"14#

Then subtract #2# from both sides to isolate the #n# term on the left side
#2ncolor(red)(cancelcolor(black)(+2)cancelcolor(green)(-2))="-"14color(green)(-2)#
#2n="-"16#

Finally divide both sides by #2# to isolate #n#
#color(green)((color(red)cancelcolor(black)2color(black)n)/color(red)cancelcolor(green)2)=color(green)(color(black)("-"16)/2)#
#n="-"8#