When 2 is added to the difference between six times a number and 5, the result is greater than 13 added to 5 times the number. Find all such numbers.

Question

When 2 is added to the difference between six times a number and 5, the result is greater than 13 added to 5 times the number. Find all such numbers.

Answer 1

(6x-5) + 2 > 5x+13             add -2 to each side

(6x-5) + 2 -2 > 5x+13 - 2    solve

6x-5 > 5x+11                      add -5x to each side

6x-5 -5x > 5x+11 -5x          solve

x - 5 > 11                           add 5 to each side

x - 5 + 5 > 11 + 5               solve

x > 16                                so the solution set includes any number greater than 16

Answer 2

(6x-5)+2 > 5x + 13

 

6x - 3 > 5x + 13

subtract 5x from both sides

x - 3 > 13

add 3 to both sides

x > 16

 

All numbers larger than 16