From Law to STEM: A lawyer’s journey from ground zero (part 4)

This is a series about a lawyer navigating her way through math / maths / mathematics / quantitative analysis.

One of the great things about being a lawyer is that you get to see if an argument plays out in real life. Algebra is similar, except it makes you VALIDATE your answer. You have to check on the spot to determine if your answers really work. Solving equations are an exercise in validated arguments; and, it is a great way to make a convincing argument.

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Today, we are going to discuss the following topics using the lawyer method of critical thinking:
* SOLVE AN EQUATION WITH MULTIPLE OPERATIONS
Think of these topics as mental tools to solve math problems.

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SOLVE AN EQUATION WITH MULTIPLE OPERATIONS
- Issue: How do we use MULTIPLE OPERATIONS to ensure the variable (literal factor / letter) is the same as the number on the other side of the equal sign?
- Rules: Get the variable alone. Use inverse (opposite) operations on both sides in the equation, with the same number. Add, subtract, multiply, divide, etc. the side with the variable and the number on the other side of the equation.
- Application:
* 3D + 10 = 70
* 3D + 10 (-10) = 70 (-10)
* 3D (÷3) = 60 (÷3)
* D = 20
- Conclusion:
* D = 20
* Validate / Check:
* 3(20) + 10 ≟ 70
* 60 + 10 ≟ 70
* 70 = 70
* Validated because 20 time 3 is 60, and 60 + 10 is 70.

Note: SOLVING EQUATIONS WHOSE UNKNOWN HAS A FRACTIONAL COEFFICIENT (Multiply the fraction by its inverse. Meaning, switch the numerator and the denominator, and multiply across.)
* 3/8x = 9
* 3/8x * (8/3) = 9 * (8/3)
* x = 9/1 * (8/3)
* x = 72/3
* x = 24