Algebra Overview

Introduction to Algebra

• Algebra is the second subject in math learned after arithmetic.
• It is considered one of the easier subjects in mathematics.
• Objective: To understand algebra in a brief overview.

What is a Variable?

• A variable is a numeric value that is unknown.
• Represented by letters, typically 'x'.
• Context-dependent: the value of 'x' can vary from one problem to another.

Multiplication Representation

• Multiplication of constants is represented with a dot (•) or an asterisk (*).
• Multiplication of a constant by a variable is shown without any symbol (e.g., 2x).

Order of Operations

• To evaluate expressions, follow the order of operations.
• The equal sign (=) indicates equivalency between two expressions.

Solving Equalities

• Example: If 2x + 4 = 16, solve for x.
• Reverse engineering method:
  1. Subtract 4 from both sides: 2x = 12
  2. Divide both sides by 2: x = 6
• Key takeaway: Operations on both sides must maintain equality.

Remembering Order of Operations

• Mnemonic: "Punch every mattress, destroy all sin"
• Reverse order: "sin all destroy mattress every punch"
• This helps recall the sequence for operations.

Understanding Inequalities

• Similar to equalities, but results indicate a range of values (larger or smaller).
• Note: Multiplying or dividing both sides by a negative number flips the inequality sign.

Example of Solving an Inequality

1. Start with an inequality: 5 < -3x + 8
2. Subtract 8 from both sides: -3 < -3x
3. Divide by -3 (flip the sign): 1 > x or x < 1.

Systems of Equations

• A system of equations consists of multiple equations with multiple variables.
• To solve, ensure that there are as many unique equations as variables.
• Example:
  1. Start with two equations.
  2. Manipulate one equation (e.g., x = y + 3).
  3. Substitute into the other equation to solve.
• Example Solution: x = 5, y = 2.

Conclusion

• Algebra skills can help in proving competency in mathematical understanding.
• Encouragement to engage with algebra, whether new or revisited knowledge.