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A number decreased by 30 is the same as 14 decreased by 3 times the number. Find the number. Explain!

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2 Answers

Let's call the unknown number x
 
Now let's decrease it by 30, that is x-30
 
Now let's write out "14 decreased by three times the number", that is 14 - 3x
 
The problem says these are the same, that is x - 30 = 14 - 3x
 
We now want to isolate, or solve for, x
 
Move the x to one side of the equation by adding 3x to both sides
 
3x + x -30 = 14 - 3x + 3x
 
4x -30 = 14
 
Now move the 30 to the right hand side by adding 30 to both sides
 
4x - 30 + 30 = 14 + 30
 
4x = 44
 
Now all we have to do to get x is divide both sides by 4
 
4x/4 = 44/4
 
x = 11

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