Question 396758
let a number be {{{x}}}

two thirds of a number is {{{(2/3)x}}}


and obtained by adding {{{7}}} to its triple {{{3x}}}


so, we have


{{{(2/3)x = 3x + 7}}}.....both sides multiply by {{{3}}}


{{{3(2/3)x = 3*3x + 3*7}}}


{{{cross(3)(2/cross(3))x = 9x + 21}}}


{{{2x = 9x + 21}}}.....add {{{-21}}}to both sides


{{{2x - 21 = 9x + 21 - 12}}}...add {{{-2x}}}to both sides


{{{2x - 21 - 2x = 9x -2x}}}


{{{cross(2x) - 21 -cross( 2x) = 7x }}}


{{{- 21  = 7x}}}......both sides multiply by {{{7}}}


{{{- 21/7  = 7x/7}}}


{{{- 3 = x}}}


check:

{{{(2/3)x = 3x + 7}}}

{{{(2/3)(-3) = 3(-3) + 7}}}

{{{2*(-3/3) = -9 + 7}}}

{{{2*(-1) = -9 + 7}}}

{{{-2 = -2}}}