How do you simplify? 5x+1(x+5+15) = x+5(5x+1+35)

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Answer 1 · 2017-03-02T02:17:17

#x=-8#

We have:

#5x+1(x+5+15)=x+5(5x+1+35)#

One way we can simplify this is to work through the Order of Operations:

#color(red)(P)# - Parentheses (also known as Brackets)
#color(blue)(E)# - Exponents
#color(green)(M)# - Multiplication
#color(green)(D)# - Division (this has the same weight as M and so I gave it the same colour)
#color(brown)(A)# - Addition
#color(brown)(S)# - Subtraction - again, same weight as A and so the same colour)

Our question has #color(red)(P)#, so let's simplify those first:

#5x+1(x+20)=x+5(5x+36)#

We've taken #color(red)(P)# as far as possible, so let's do #color(green)(M)# - by doing the distributions:

#5x+x+20=x+25x+180#

And now #color(brown)(A)#

#6x+20=26x+180#

We've simplified the expression, so now we need a bit of algebra. Let's move terms so we have #x# terms on one side and non-#x# terms on the other:

#6xcolor(red)(-26x-20)+20=26xcolor(red)(-26x-20)+180#

#-20x=160#

#x=160/(-20)=-8#

Now let's check our answer:

#5(-8)+1((-8)+5+15)=(-8)+5(5(-8)+1+35)#

#-40+1(12)=(-8)+5(-40+36)#

#-28=(-8)+5(-4)#

#-28=(-8)-20#

#-28=-28color(white)(000)color(green)sqrt#

~~~~~~~~~~

We could also have done this:

#5x+1(x+5+15)=x+5(5x+1+35)#

distribute first:

#5x+x+5+15=x+25x+5+175#

then combine like terms:

#6x+20=26x+180#

and then solve in the normal way.