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

Mar 17, 2016

Break the problem into two stages:
$\textcolor{w h i t e}{\text{XXX}}$-simplify the quotient
$\textcolor{w h i t e}{\text{XXX}}$-divide the simplified quotient by 2

Explanation:

Simplifying the quotient
Given
$\textcolor{w h i t e}{\text{XXX}} x \left(5 - 3\right) - 10 x + 6 - 8$
Using the order of operation (e.g. PEDMAS)
$\textcolor{w h i t e}{\text{XXX}} = x \left(2\right) - 10 x + 6 - 8$

$\textcolor{w h i t e}{\text{XXX}} = 2 x - 10 x + 6 - 8$

$\textcolor{w h i t e}{\text{XXX}} = - 8 x + 6 - 8$

$\textcolor{w h i t e}{\text{XXX}} = - 8 x - 2$

Divide the simplified quotient by $2$
$\textcolor{w h i t e}{\text{XXX}} \left(- 8 x - 2\right) \div 2$

$\textcolor{w h i t e}{\text{XXX}} = - \left(8 x \div 2\right) - \left(2 \div 2\right)$

$\textcolor{w h i t e}{\text{XXX}} = - 4 x - 1$

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:
$\textcolor{w h i t e}{\text{XXX}} 2 x - 10 x + 6 - 8 \div 2$

$\textcolor{w h i t e}{\text{XXX}} = 2 x - 10 x + 6 - 4$

$\textcolor{w h i t e}{\text{XXX}} = - 8 x + 6 - 4$

$\textcolor{w h i t e}{\text{XXX}} = - 8 x + 2$

Mar 17, 2016

$- 8 x + 2$

Explanation:

$5 x - 3 x - 10 x + 6 - 8 \div 2$

$- 8 x + 6 - 4$

$- 8 x + 2$

Aug 6, 2017

$- 8 x + 2$

Explanation:

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

$\textcolor{b l u e}{x \left(5 - 3\right)} \text{ "color(red)(-10x)" " color(green)(+6)" " color(purple)(-8div2)" } \leftarrow$ there are 4 terms

$= \text{ "color(blue)(x(2))" " color(red)(-10x) " "color(green)(+6) " } \textcolor{p u r p \le}{- 4}$

$= \text{ "color(blue)(2x)" " color(red)(-10x) " "color(green)(+6) " "color(purple)(-4)" } \leftarrow$collect like terms

$= - 8 x + 2$