Question

test it: equivalent expressions
expression a: $3x + 4$
expression b: $2 + 3x + 2$
which statement can be used to show that these expressions are equivalent?
1 of 4 questions

• each expression includes the term $3x$.
• $3x + 4$ can be rewritten as $2 + 3x + 2$ using the distributive property.
• both expressions involve addition.
• the expressions name the same number regardless of the value of $x$.

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Explanation:

• Option 1: Just having the same term \(3x\) doesn't prove equivalence (e.g., \(3x + 4\) and \(3x+5\) have \(3x\) but aren't equivalent).
• Option 2: The distributive property isn't used here. We combine like terms (\(2 + 2=4\)) to rewrite \(2 + 3x+2\) as \(3x + 4\), not the distributive property.
• Option 3: Both involving addition doesn't mean they are equivalent (e.g., \(3x + 4\) and \(3x+5\) both involve addition but aren't equivalent).
• Option 4: By the definition of equivalent expressions, two expressions are equivalent if they name the same number for all values of the variable(s). So checking that they name the same number regardless of \(x\) shows equivalence.

Answer:

The expressions name the same number regardless of the value of \(x\)