Algebra Class: Grouping Symbols & Simplification

Grouping Symbols and Simplification Techniques

• Q, R, S, T Definitions: Q = 7m + 3n, R = 11 - 2m, S = n + 5, T = -m - 3n + 8. These variables are used across multiple simplification problems.

• Simplifying Expressions:

  • Q - [R + S] - T simplifies to 10m - 5n + 24.
  • [Q - R] + [S - T] results in 10m + 7n - 14.

• Combining Like Terms:

  • (3x + 5) + (2x - 9) - (4x + 3) reduces to x - 7.
  • R - [S + T] yields -m + 2n - 2.

• Negative and Positive Operations:

  • Simplifying -(-2a + 13) + (-9a - 2) - (-7a - 3) gives a result of -12.

• Additional Simplifications:

  • R - S + T combines to -3m - 4n + 14.
  • 2m - [n - (m - 2n)] simplifies to 3m - 3n.
  • Q + S - T results in 8m + 7n - 3.

Advanced Simplification Cases

• Multi-layered Brackets:

  • Simplifying 3j - {2k - [5h - (3j + k)]} leads to 5h - 3k.
  • a - {5b - [a - (3b - 2c) + c - (a - 2b - c)]} simplifies to a - 6b + 4c.

• Linear Combinations:

  • (x - y + 1) - (x + y - 1) results in -2y + 2.
  • Similar structure in {n - 1 - [n - 1 - (n - 1)]} simplifies to n - 1.
  • Final case n - {1 - [n - (1 - n) - 1]} reduces to 3n - 3.

Key Takeaways

• Grouping symbols and careful distribution is essential for simplifying complex algebraic expressions.
• Understanding how to manipulate positive and negative signs is critical in arriving at the correct solutions.
• Practice with various forms of expressions enhances capabilities in algebra simplification.