How do you simplify #-1/20 ( 5z - 4w ) -6 ( -1/30w - 1/24z ) #?

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Answer 1 · 2016-04-24T14:19:40

#2/5w#

Consider:#" "-1/20(5z-4w)#

It is not normally written this way but I am doing so to assist understanding:

Write as #" "(-1)xx1/20xx(5z-4w)#

Multiply everything inside the brackets by #1/20#

#" "(-1)xx(5/20z-4/20w)#

Multiply everything inside the brackets by #(-1)#

#" "-5/20z+4/20w#

But #" "(5-:5)/(20-:5)=1/4" and "(4-:4)/(20-:4)=1/5# giving

#" "color(blue)(-1/4z+1/5w)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider#" "-6(-1/30w-1/24z)#

Multiply everything inside the brackets by -6

#" "+6/30w+6/24z#

But #" "(6-:6)/(30-:6)=1/5" and "(6-:6)/(24-:6)=1/4# giving

#" "color(blue)(+1/5w+1/4z)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

#" "-1/4z+1/5w+1/5w+1/4z#

Collecting like terms

#" "-1/4z+1/4z+1/5w+1/5w#

#" "0z+2/5w#

#" "color(blue)(2/5w)#