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Number magic

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Pick a number from 1 to 9 (0<x<10). Multiply it by 2. Then add 3 to the result. Now multiply this number by 50, then add 1853 and subtract the year of you birth. You now should have a 3 digit number. The first digit is the number you picked above, and the last 2 digits are your age after your birthday this year (2003).
How is this possible? What is the algebraic explanation behind this?

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Solution Summary

This shows the algebra behind one of many number tricks. The positive and negative expressions are compared.

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Lets call number "x", then multiply by 2 you get "2x", add 3, you get "2x+3", multiply by 50 you get "100x+150" add 1853 you get "100x+2003".
Assume your date of birth is a four digit number starting with 1900 and ending in "ab": "19ab" (no one reading this is born before that!), ...

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