Advanced Equation Types - Page 2

The second page delves into more complex equation types, including null product equations and equations of the form x² = a.

Definition: Null Product Rule - If a product of factors equals zero, then at least one of the factors must be zero.

Example: Solving (2x + 3)(5 - x) = 0: Either 2x + 3 = 0 or 5 - x = 0 x = -3/2 or x = 5 The equation has two solutions: -3/2 and 5

Highlight: For equations of type x² = a:

• If a < 0, the equation has no real solutions
• If a = 0, the equation has one solution: 0
• If a > 0, the equation has two solutions: √a and -√a

Example: For x² = 9: Since 9 > 0, the equation has two solutions: √9 = 3 and -√9 = -3

Understanding Mathematical Equations - Page 1

The first page introduces fundamental concepts of mathematical equations and their solutions. The content focuses on defining equations and demonstrating how to solve first-degree equations with one unknown variable.

Definition: An equation is an equality between two expressions, called members of the equation, containing an unknown number represented by a letter.

Highlight: Solving an equation means finding all values of the unknown variable that make the equality true.

Example: For the equation 2x + 5 = x + 3: To verify if 1 is a solution: If x = 1: 2(1) + 5 = 7 1 + 3 = 4 Therefore, 1 is not a solution as 7 ≠ 4

Vocabulary: First-degree equation with one unknown - An equation where there is only one unknown variable raised to the first power.

Example: Solving the equation 5x - 2x = -9: 3x = -9 x = -3 The solution is -3