Question 214847
Four times the difference of a number and 2 is the same as 2 increased by four times the number plus twice the number.  Find the number.  


Step 1.  Let n be the number.


Step 2.  Let n-2 is the difference between the number and 2.


Step 3.  Let 4(n-2) is four times the difference between the number and 2


Step 4.  Let 2+4n+2n be 2 increased by 4 times the number plus twice the number 


where 4n is four times the number and 2n is twice the number.


Step 5.  Set expressions in Step 3 and 4 equal.


{{{4(n-2)=2+4n+2n=2+6n}}}


{{{4n-8=2+6n}}}


Subtract 4n to both sides of the equation


{{{4n-8-4n=2+6n-4n}}}


{{{-8=2+2n}}}


Subtract -2 to both sides of the equation to get solve for n


{{{-8-2=2+2n-2}}}


{{{-10=2n}}}


Divide by 5 to both sides of equation to get n


{{{-10/2=2n/2}}}


{{{-5=n}}}


{{{n=-5}}}


Step 6.  ANSWER.  The number is -5.


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J