Question 230584
When 2 is added to the difference between 6 times a number and 5, the result is greater than 13 added to 5 times the number find all such numbers?


Step 1.  Let x be the number


Step 2.  Let 6x be six times the number.


Step 3.  Let 2+6x-5=6x-3 when 2 is added to the difference between 6x a number and 5.


Step 4.  Let 6x-3=13+5x since the result is 13 added to 5 times the number.


Step 5.  Solving 6x-3=13+5x leads to the following steps


Add 3-5x to both sides of the equation to get only x terms on one side and only numbers on the other side


{{{6x-3+3-5x=13+5x+3-5x}}}


{{{x=16}}}


Step 6. Check solution {{{x=16}}} with Equation in Step 5 {{{6x-3=13+5x}}}


{{{6*16-3=13+5*16}}}


{{{96-3=13+80}}}


{{{93=93}}} which is a true statement


Step 7.  ANSWER:  The number is 16.


I hope the above steps were helpful.


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Respectfully,
Dr J

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