Mathematics Notes on Expanding Brackets and Solving Equations

Equation Solving

• Given: x - 4 = 9

• To find the value of x:

• Add 4 to both sides:

  • x - 4 + 4 = 9 + 4

  • Simplifies to: x = 13

Expanding Brackets

• Understanding expansion:

• To expand means to make something bigger or to simplify expressions.

• Example context: the addition of variables and coefficients.

• Definition of expanding brackets:

• Multiply the term outside the bracket by each term inside the bracket.

• Example to expand:

• Given: 3(2x + 5)

• Outside term: 3

• Inside terms: 2x and 5

  • Steps to expand:

  • Multiply 3 with each inside term:

    • 3 * 2x = 6x

    • 3 * 5 = 15

  • Result: 6x + 15

General Concept of Variables

• 2x is not a specific number.

• It means two times some unknown value (denoted as x).

• Without an equation equating to a specific value, it simply remains as it is.

Practical Application of Expanding

• It’s more about practicing the concept rather than solving for x.

• Example: Expanding the term 2(2x + 2):

• Multiply:

  • 2 * 2x = 4x

  • 2 * 2 = 4

• Result will be: 4x + 4

Review of Operations

• Discuss counts and multiples:

• 3, 6, 9, etc., for understanding multiplication tables (e.g., multiples of 3).

• Relate multiplication of integers to visual counts (both positively and negatively).

Engagement in Math Concepts

• Reinforce learning through various approaches (saying, visual representations).

• Using methods to ensure understanding, such as focusing on how to manage and manipulate expressions without focusing on finding unknowns yet.

• Emphasize practice through examples, which helps strengthen comprehension of the subject matter.