SOLUTION: 3 times the sum of twice a number and 6 is 4 times 2 less than the number. find the number.

Question 55455: 3 times the sum of twice a number and 6 is 4 times 2 less than the number. find the number.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
The trickiest part about these kinds of problems is, of course, translating the prose to algebra. Let n = the number.
Three times (3X) the sum (+) of twice a number (2n) and 6...3(2n+6) is (=) four times (4X) two less than the number (n-2)...4(n-2). Putting it all together:
3(2n+6) = 4(n-2) Simplify and solve for n.
6n+18 = 4n-8 Collect like-terms.
2n = -26 Divide both sides by 2.
n = -13
Check:
3(2(-13)+6) = 3(-26+6) = 3(-20) = -60
4(-13-2) = 4(-15) = -60
The number is -13
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