MTPPT2 Equations

Engineering Mathematics 1 Summary

• Linear Equations in One Variable: Focuses on solving equations with one variable using the following key components:

  • Objectives: Solve linear equations, recall properties of equality.

  • Definitions:

    • Equality: Relationship of equal value.

    • Properties: Rules for balancing equations.

    • Equivalent Equations: Equations with the same solution.

  • Properties of Equality:

    • Addition Property: a − b = c → a = c + b.

    • Subtraction Property: a + b = c → a = c - b.

    • Multiplication Property: a = b → ac = bc (c ≠ 0).

    • Division Property: a = b, b ≠ 0 → a/b = c/b → a = c/b.

  • Distributive Property: a(b + c) = ab + ac.

  • Equation Types: Linear (e.g., 2x + 3 = 11) vs. Not Linear (e.g., 2x + 3y = 11).

  • Solving Steps: Simplify, isolate variable, and simplify again.

  • Application Problems: Involves real-world problems using algebraic equations such as hiker problems, coin problems, and more with varied solution strategies including quadratic equations and discriminants.