The expression
[beautiful math coming... please be patient]
$\,2x + 1\,$
represents the sequence of operations
‘take a number, multiply by
[beautiful math coming... please be patient]
$\,2\,$, then add
[beautiful math coming... please be patient]
$\,1\,$’.
The expression
[beautiful math coming... please be patient]
$\,2(x+1)\,$
represents the sequence of operations
‘take a number, add
[beautiful math coming... please be patient]
$\,1\,$,
then multiply by
[beautiful math coming... please be patient]
$\,2\,$’.