Overview

This topic introduces basic algebraic skills used to manipulate expressions, solve equations, and understand the behavior of functions. You’ll learn how to evaluate, simplify, and solve linear equations, and explore how functions are represented symbolically, numerically, and graphically.

Key Concepts and Structures

• Algebraic Expressions: Combinations of variables, constants, and operations. Example: 2x + 5
• Linear Equations: Equations of the form ax + b = c. Solved using inverse operations to isolate the variable.
• Inequalities: Use symbols like <, >, ≤, ≥. Solve similarly to equations, but reverse the inequality if multiplying/dividing by a negative number.
• Systems of Equations: Two or more equations solved simultaneously. Methods include graphing, substitution, and elimination.
• Functions: A relationship where each input has exactly one output. Common forms: f(x) = 2x + 1
• Evaluating Functions: Substitute a value for the variable. Example: f(3) = 2(3) + 1 = 7
• Representations of Functions: Functions can be described with equations, tables, graphs, or words.
• Growth Patterns: Recognize and interpret linear (constant rate) and exponential (multiplicative rate) changes.

Step-by-Step Example

Problem: Solve 3x - 7 = 2x + 5

Step 1: Move variables to one side:
3x - 2x = 5 + 7

Step 2: Simplify:
x = 12

Final Answer: x = 12

Quick Tip