Question

How do you solve `8x + 39 = 2x - 15`?

Answer 1

Showing first principle methods in high detail. These methods will never let you down!

`x=-9`

Explanation:

The objective is to have just one `x` and for it to be on one side of the = and everything else to be on the other side. In this form it is saying: the value of x is ....

`color(brown)("Using first principles from which the shortcuts are derived")`

With practice you will recognise the shortcuts and start to use them with confidence.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(green)("Subtract "color(blue)(2x)" from both sides")`

`" "color(brown)(8x+39color(blue)(-2x)=2x-15color(blue)(-2x))`

`" "8x-2x+39=2x-2x-15`

'...............................................................................................

`color(green)("But "8x-2x=6x" and "2x-2x=0)`

`" "6x+39=0-15`
'.........................................................................
`color(green)("Subtract "color(blue)(39)" from both sides")`

`" "color(brown)(6x+39color(blue)(-39)=-15color(blue)(-39))`

'........................................................................

`color(green)("But "39-30=0" and "-15-39 =-54)`

`" "6x+0=-54`

`" "6x=-54`
'...................................................................
`color(green)("Divide both sides by "color(blue)(6))`

`" "color(brown)(6xcolor(blue)(-:6)=(-54)color(blue)(-:6))`

`" "color(brown)(6/(color(blue)(6))xx x =(-54)/(color(blue)(6))`
'..................................................................
`color(green)("But "6/6=1)`

`" "x=-54/6`
'.............................................................
`color(green)("But "54/6=(54-:6)/(6-:6)= 9/1)`

`color(magenta)(" "x=-9)`