Algebraic Expressions, Identities and Formulae

Algebraic Expressions, Identities and Formulae

Secondary 1

Mei claims: \[3(x+2)-2(x-1)=x+4.\] Raj claims:\[3(x+2)-2(x-1)=2x+8.\]

  1. Simplify the original expression and explain the error in each claim.

  2. Raj tests \(x=0\). Show why his answer appears correct for this value.

  3. Choose another value of \(x\) that disproves Raj’s claim. Explain why one successful numerical check does not prove that two expressions are always equal.

Solution:

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Answer:(a) \(x+8\); Mei’s sign error: \((-2)(-1)=+2\); Raj’s coefficient error: \(3x-2x=x\). (b) At \(x=0\), both give \(8\), masking Raj’s error. (c) At \(x=1\), the original gives \(9\), but Raj’s gives \(10\); agreement at one value does not prove equality for all values.

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