Section 1.1: Linear Equations & Inequalities
This section reviews linear equations and inequalities, focusing on their structure, solution methods, and applications. Understanding these is crucial for all subsequent Algebra II topics.
Example 1: Solving a Linear Equation
Solve for x: 3x - 7 = 11.
Step 1: Add 7 to both sides → 3x = 18
Step 2: Divide both sides by 3 → x = 6
Example 2: Solving a Linear Inequality
Solve for y: 5y + 2 ≤ 17.
Step 1: Subtract 2 from both sides → 5y ≤ 15
Step 2: Divide both sides by 5 → y ≤ 3
Practice Problems
- Solve for x: 4x + 9 = 25
- Solve for y: 7y - 5 ≥ 16
- Find x: 2(x - 3) + 5 = 13
- Solve: 6 - 3x < 12
- Word problem: A phone plan costs $20 plus $0.10 per text. If total bill is $35, how many texts were sent?