Question 658776
step:

1) {{{ rate 1 < rate 2 }}}

2) let x be the # of miles: {{{ 42 + .12x < 84 + .06x}}}

3) make .12 and .06 whole numbers by moving ALL decimals (including 42 and 84)two spaces to the right: {{{ 4200 + 12x < 8400 + 6x }}}

4) subtract 6x from both sides: {{{ 4200 + 12x -6x < 8400 + 6x - 6x }}}

5){{{ 4200 + 6x < 8400 }}}

6) subtract 4200 from both sides:  {{{4200 - 4200 + 6x < 8400 - 4200}}}

7) {{{6x < 4200}}}

8) devide both sides by 6 to get x by itself: {{{ 6x/6 < 4200/6 }}}

9) answer is greater than 700 miles   {{{ x<700 }}}