Which of the following is not equivalent to this expression? * 2m + 10m +…

Which of the following is not equivalent to this expression? * 2m + 10m + 14 + 3

Direct answer: The expression simplifies to 12m + 17, so any choice not equal to 12m + 17 (for example 12m + 7) is NOT equivalent.

  1. Identify like terms and combine:
  • Combine the m-terms: $$2m + 10m = 12m.$$
  • Combine the constant terms: $$14 + 3 = 17.$$
  1. Write the simplified result:
  • $$2m + 10m + 14 + 3 = 12m + 17.$$
  1. How to check equivalence (useful if you have multiple-choice options):
  • An expression is equivalent iff it simplifies to the same algebraic form for all m.
  • Quick check: substitute a value for m (e.g., $m=1$). The original expression gives

$$2(1)+10(1)+14+3 = 2+10+14+3 = 29.$$
Any equivalent expression must also equal 29 when $m=1$.

  • Example: $12m+17$ at $m=1$ gives $12(1)+17=29$ (equivalent).

Example non-equivalent: $12m+7$ at $m=1$ gives $19$ (not equivalent).

  1. Examples of expressions equivalent to $12m+17$:
  • $12m+17$ (obvious),
  • $(2m+10m)+(14+3)$ (re-grouping),
  • $6(2m)+17$ or $3(4m)+17$ (same value but written with a factor).
  1. Examples of expressions NOT equivalent:
  • $12m+7$ (different constant),
  • $11m+17$ (different coefficient of m),
  • $12m-17$ (different sign on constant),
  • any expression that does not simplify to $12m+17$ for every m.

Summary: The simplified form is 12m + 17; any expression that does not equal this (e.g., 12m + 7) is not equivalent.

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