Jaden starts with a number. He adds 3 to the number, then doubles the result. Finally, he subtracts 7. If he ended with 9, what number did he start with?

1 Answer
smendyka
Apr 5, 2018

See a solution process below:

Explanation:

First, let's call the number Jaden started with: #n#

He adds 3 to the number #=> n + 3#

Then doubles the result #=> 2(n + 3)#

Finally, he subtracts 7 #=> 2(n + 3) - 7#

He ended with 9 #=> 2(n + 3) - 7 = 9#

We can solve this equation by first adding #color(red)(7)# to each side of the equation to isolate the term with parenthesis while keeping the equation balanced:

#2(n + 3) - 7 + color(red)(7) = 9 + color(red)(7)#

#2(n + 3) - 0 = 16#

#2(n + 3) = 16#

Next, divide each side of the equation by #color(red)(2)# to eliminate the need for parenthesis while keeping the equation balanced:

#(2(n + 3))/color(red)(2) = 16/color(red)(2)#

#(color(red)(cancel(color(black)(2)))(n + 3))/cancel(color(red)(2)) = 8#

#n + 3 = 8#

Now, subtract #color(red)(3)# from each side of the equation to solve for #n# while keeping the equation balanced:

#n + 3 - color(red)(3) = 8 - color(red)(3)#

#n + 0 = 5#

#n = 5#

Jaden started with the number: #color(red)(5)#

He adds 3 to the number #=> color(red)(5) + 3 = 8#

Then doubles the result #=> 2 xx color(red)(8) = 16#

Finally, he subtracts 7 #=> color(red)(16) - 7 = 9#

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