Questions and Answers
Simplify Q - [R + S] - T, where Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.
10m - 5n + 24
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Simplify [Q - R] + [S - T], where Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.
10m + 7n - 14
Simplify (3x + 5) + (2x - 9) - (4x + 3).
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Simplify R - [S + T], where R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.
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Simplify -(-2a + 13) + (-9a - 2) - (-7a - 3).
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Simplify R - S + T, where R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.
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Simplify 2m - [n - (m - 2n)].
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Simplify Q + S - T, where Q = 7m + 3n, S = n + 5, and T = -m - 3n + 8.
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Simplify 3j - {2k - [5h - (3j + k)]}.
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Simplify a - {5b - [a - (3b - 2c) + c - (a - 2b - c)]}.
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Simplify (x - y + 1) - (x + y - 1).
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Simplify {n - 1 - [n - 1 - (n - 1)]}.
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Simplify n - {1 - [n - (1 - n) - 1]}.
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Study Notes
Grouping Symbols and Simplification Techniques
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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.
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Simplifying Expressions:
- Q - [R + S] - T simplifies to 10m - 5n + 24.
- [Q - R] + [S - T] results in 10m + 7n - 14.
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Combining Like Terms:
- (3x + 5) + (2x - 9) - (4x + 3) reduces to x - 7.
- R - [S + T] yields -m + 2n - 2.
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Negative and Positive Operations:
- Simplifying -(-2a + 13) + (-9a - 2) - (-7a - 3) gives a result of -12.
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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
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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.
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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.
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Description
Test your understanding of grouping symbols and simplification techniques in algebra with this quiz. It covers various methods for simplifying expressions, combining like terms, and handling negative and positive operations. Challenge yourself with both basic and advanced simplification problems!
