How do you simplify #-6(7 + x)#?

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Answer 1 · 2016-05-07T20:59:15

#-42-6x#

#color(blue)("Detailed explanation building up to the shortcut method")#

When it is written in the form #-6(7+x)# it is the same as #(-6)xx(7+x)#

I will deal with the negative aspect of this in a while.

This means that you have 6 lots of #(7+x)#

So you have 6 lots of 7 and #6xx7=42#

You also have 6 lots of x and #6xx x =6x#

So, ignoring the negative part of -6,

#6(7+x)=42+6x#

#color(brown)("Everything inside the bracket is multiplied by 6")#

#color(brown)("However, we have "-6(7+x))#

This is the same as #(-1)xx6xx(7+x)#

Multiply everything inside the bracket by #(-1)# giving:

#6xx(-7-x)#

Now multiply everything inside the bracket by 6 giving:

#-42-6x#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Shortcut method")#

Given: #-6(7+x)#

#color(brown)("Multiply everything inside the bracket by -6")#

#-42-6x#