How do you solve #9(n + 3) = 7n-3#?

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Answer 1 · 2016-08-17T14:51:41

#n=-15#

Given:#" "9(n+3)=7n-3#

#color(purple)("Using first principles rather than the shortcuts")#

Multiply everything inside the bracket by the 9 that is outside the brackets, giving:

#(9xxn)+(9xx3)=7n-3#

#9n+27" "=" "7n-3#

Subtract #color(blue)(7n)# from both sides

#color(brown)(9ncolor(blue)(-7n)+27" "=" "7ncolor(blue)(-7n)-3)#

#2n+27=0-3#

Subtract #color(blue)(27)# from both sides

#color(brown)(2n+27color(blue)(-27)=-3color(blue)(-27))#

#2n+0=-30#

Divide both sides by #color(blue)(2)#

#color(brown)(2/(color(blue)(2))xxn=-30/(color(blue)(2))#

But #2/2=1# giving:

#n=-15#