Question

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

Answer 1

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`

Answer 2

`-8x+2`

Explanation:

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

`-8x +6 -4`

`-8x +2`

Answer 3

`-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`