Which expression is NOT equivalent to 2q + 24?
Understand the Problem
The question is asking us to identify which expression is not equivalent to the expression 2q + 24. This involves understanding algebraic equivalence and potentially simplifying or manipulating expressions to see if they match the given one.
Answer
C
Answer for screen readers
C
Steps to Solve
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Simplify option A Simplify the expression $2(q+12)$ by distributing the 2. $2(q+12) = 2 \cdot q + 2 \cdot 12 = 2q + 24$
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Simplify option B Simplify the expression $2(q+2) + 20$ by distributing the 2 and then combining like terms. $2(q+2) + 20 = 2 \cdot q + 2 \cdot 2 + 20 = 2q + 4 + 20 = 2q + 24$
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Simplify option C The expression is $2(q+22) - 2$. Distribute the 2 and combine like terms. $2(q+22) - 2 = 2 \cdot q + 2 \cdot 22 - 2 = 2q + 44 - 2 = 2q + 42$
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Simplify option D The expression is $6(q+4) - 4q$. Distribute the 6 and combine like terms $6(q+4) - 4q = 6 \cdot q + 6 \cdot 4 - 4q = 6q + 24 - 4q = 6q - 4q + 24 = 2q + 24$
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Identify the non-equivalent expression Compare the simplified forms of options A, B, C, and D with the original expression $2q + 24$. A: $2q + 24$ B: $2q + 24$ C: $2q + 42$ D: $2q + 24$ Option C is not equivalent to $2q + 24$.
C
More Information
Algebraic equivalence means that two expressions are equal for all values of the variable. In this problem, only one of the options, C, simplifies to an expression that is different from the original expression $2q + 24$.
Tips
- Not distributing correctly: A common mistake is failing to properly distribute the number outside the parentheses to both terms inside. For example, in option A, you must multiply both $q$ and $12$ by $2$.
- Incorrectly combining like terms: Make sure to only add or subtract terms that have the same variable part. For example, you can combine $6q$ and $-4q$ in option D, but you cannot combine $2q$ and $24$.
- Forgetting order of operations: Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.
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