How do you simplify #x(5-3)-10x+6-8-:2#?

3 Answers
Mar 17, 2016

Break the problem into two stages:
#color(white)("XXX")#-simplify the quotient
#color(white)("XXX")#-divide the simplified quotient by 2
See also alternate Interpretation below first answer

Explanation:

Simplifying the quotient
Given
#color(white)("XXX")x(5-3)-10x+6-8#
Using the order of operation (e.g. PEDMAS)
#color(white)("XXX")=x(2)-10x+6-8#

#color(white)("XXX")=2x-10x+6-8#

#color(white)("XXX")=-8x+6-8#

#color(white)("XXX")=-8x-2#

Divide the simplified quotient by #2#
#color(white)("XXX")(-8x-2)div2#

#color(white)("XXX")=-(8xdiv2) -(2div2)#

#color(white)("XXX")=-4x-1#

Alternate Interpretation
I assumed that the division (using the #div# symbol) was to be applied to the entire preceding expression.
Technically this should not be true.

Applying strict PEDMAS to the entire expression would give:
#color(white)("XXX")2x-10x+6-8div2#

#color(white)("XXX")=2x-10x+6-4#

#color(white)("XXX")=-8x+6-4#

#color(white)("XXX")=-8x+2#

Mar 17, 2016

#-8x+2#

Explanation:

#5x-3x-10x+6 -8 div2#

#-8x +6 -4#

#-8x +2#

Aug 6, 2017

#-8x+2#

Explanation:

Count the number of terms first and the simplify each term separately. Combine any like terms in the last step:

#color(blue)(x(5-3)) " "color(red)(-10x)" " color(green)(+6)" " color(purple)(-8div2)" "larr# there are 4 terms

#=" "color(blue)(x(2))" " color(red)(-10x) " "color(green)(+6) " "color(purple)(-4)#

#=" "color(blue)(2x)" " color(red)(-10x) " "color(green)(+6) " "color(purple)(-4)" "larr#collect like terms

#=-8x+2#