Question

How do you solve `3(x+5) +6 = 15`?

Answer 1

`color(blue)(x=-2`

Explanation:

`3 ( x+5) + 6 = 15`

`color(blue)((3)) * ( x+5) + 6 = 15`

`color(blue)((3)) * ( x) + color(blue)((3)) *(5) + 6 = 15`

`3x + 15 + 6 = 15`

`3x + 21 = 15`

`3x = 15 - 21`

`3x = -6`

`x = (-6)/3`

`color(blue)(x=-2`

Answer 2

Just in case you need further explanation

`x=-2`

Explanation:

Consider `3(x+5)` This means that you have 3 lots of `(x+5)`

Which is: `x+5`
`" "x+5`
`" "ul(x+5) " "larr" add`
`" "3x+15`

`color(green)("Basically you multiply everything inside the brackets by 3")`

So `" "color(brown)(3(x+5)+6=15)" "color(blue)(->" "3x+15+6=15`

`3x+21=15`

'~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(green)("To get rid of the 21 on the left subtract 21 from both sides")`

`3x+21-21=15-21`

`3x+0=-6`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(green)("To get rid of the 3 from "3x" divide both sides by 3")`

`3/3 xx x=-6/3`

But `3/3=1" and "1xx x =x`

`x=-2`