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Mathematics - Algebra - Applications

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In your work or personal life, what are some common applications of algebra? If you don't have first-hand knowledge of these applications, then how do you perceive it being used? If you're feeling really motivated, please give an example equation with your example.

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A complete and neat solution with necessary examples of common application of algebra with equations is provided in the attached file.

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In real life, we use algebra all the time.

(1) When filling my car up with gas I use algebra. Lets say I only have $30 to spend on gas today and gas is $3 a gallon. How many gallons can I buy?
Let x = Number of gallons of gas
Then x = 30/3 = 10 gallons

(2) Algebra is ...

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