MAT112: 1.1 Review on Algebra

Introduction

This tutorial is designed to provide a clear and structured review of key algebra concepts covered in the video "MAT112: 1.1 Review on Algebra." Understanding these fundamentals is essential for success in algebra and other advanced mathematics courses.

Step 1: Understanding Variables and Expressions

• Definition: A variable is a symbol used to represent a number in mathematical expressions and equations.
• Example: In the expression ( 3x + 5 ), ( x ) is the variable.
• Tips:
  • Always identify the variables in your expressions and what they represent.
  • Practice simplifying expressions by combining like terms.

Step 2: Mastering the Order of Operations

• Order of Operations: Remember the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
• Steps:
  1. Solve expressions inside parentheses first.
  2. Calculate exponents.
  3. Perform multiplication and division from left to right.
  4. Finally, do addition and subtraction from left to right.
• Common Pitfalls: Skipping steps or misapplying the order can lead to incorrect answers. Always follow the order strictly.

Step 3: Solving Linear Equations

• Definition: A linear equation is an equation of the first degree, meaning it has no exponents greater than one.
• General Form: ( ax + b = c )
• Steps to Solve:
  1. Isolate the variable ( x ) by performing inverse operations.
  2. Subtract ( b ) from both sides: ( ax = c - b ).
  3. Divide both sides by ( a ): ( x = \frac{c - b}{a} ).
• Example: Solve ( 2x + 3 = 7 ):
  • Subtract 3: ( 2x = 4 )
  • Divide by 2: ( x = 2 )

Step 4: Working with Inequalities

• Inequalities: Similar to equations, but they show a range of values rather than a single solution.
• Symbols: Understand the different symbols: ( <, >, \leq, \geq ).
• Steps to Solve:
  1. Treat them like equations, using inverse operations.
  2. When multiplying or dividing by a negative number, remember to reverse the inequality sign.
• Example: Solve ( -2x > 6 ):
  • Divide by -2 and reverse the sign: ( x < -3 )

Step 5: Learning Function Basics

• Definition: A function is a relation that assigns exactly one output for each input.
• Notation: Functions are often written as ( f(x) ).
• Key Points:
  • Understand domain (input values) and range (output values).
  • Graphing functions can help visualize their behavior.

Conclusion

In this tutorial, we covered essential algebra concepts, including variables, the order of operations, solving linear equations and inequalities, and the basics of functions. Mastering these topics lays the groundwork for more advanced mathematical studies. To further enhance your understanding, consider practicing problems related to each step and reviewing examples from your textbook or online resources.