Page 1: Fundamental Steps in Equation Solving

The page introduces core concepts for solving algebraic equations through a methodical approach. It emphasizes performing identical operations on both sides of an equation to maintain balance and reach a solution. The process involves identifying terms, isolating variables, and verifying answers.

Definition: An equation remains balanced when the same mathematical operation is performed on both sides.

Example: In solving 3x + 7 = 16:

1. Subtract 7 from both sides: 3x = 9
2. Divide both sides by 3: x = 3
3. Check solution by substituting back: 3(3) + 7 = 16

Highlight: The three main steps for solving equations are:

1. Subtract or add to isolate variable terms
2. Multiply both sides by the denominator to eliminate fractions
3. Divide by the coefficient to solve for the variable

Vocabulary:

• Coefficient: The number multiplied by a variable (e.g., 3 in 3x)
• Term: A single number, variable, or product of numbers and variables
• Solution: The value that makes the equation true when substituted for the variable

The page concludes with multiple practice examples demonstrating these principles, including equations with fractions and different coefficient values, reinforcing the systematic approach to equation solving.