Question
Select all the expressions equivalent to \( 2(x+ \) 1. \( 2 \cdot(x+3) \) 2. \( (x+3) 2 \) 3. \( 2 \cdot x+2 \cdot 3 \) 4. \( 2 \cdot x+3 \) 5. \( (2 \cdot x)+3 \) 6. \( (2+x) 3 \)
Ask by Lynch Hart. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equivalent expressions are options 1, 2, and 3.
Solution
We begin with the expression 2(x+3). To see which ones are equivalent, we can simplify 2(x+3) by distributing the 2:
2(x+3) = 2·x + 2·3 = 2x + 6
Now check each option:
1. 2 · (x+3): This is the same as the given expression.
2. (x+3) 2: Since multiplication is commutative, this is also 2·(x+3).
3. 2 · x+2 · 3: This simplifies to 2x+6.
4. 2 · x+3: This simplifies to 2x+3, which is not equal to 2x+6.
5. (2 · x)+3: This is also 2x+3, so it does not match.
6. (2+x) 3: This means 3·(2+x) = 3x+6, which is not equal to 2x+6.
Thus, the expressions equivalent to 2(x+3) are options 1, 2, and 3.
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To find expressions equivalent to \( 2(x + 3) \), we first expand it to \( 2x + 6 \). Now, let's evaluate each option: 1. \( 2 \cdot (x+3) = 2x + 6 \) (equivalent) 2. \( (x+3) \cdot 2 = 2x + 6 \) (equivalent) 3. \( 2 \cdot x + 2 \cdot 3 = 2x + 6 \) (equivalent) 4. \( 2 \cdot x + 3 = 2x + 3 \) (not equivalent) 5. \( (2 \cdot x) + 3 = 2x + 3 \) (not equivalent) 6. \( (2 + x) \cdot 3 = 3x + 6 \) (not equivalent) Thus, the expressions that are equivalent to \( 2(x + 3) \) are: - \( 2 \cdot (x+3) \) - \( (x+3) \cdot 2 \) - \( 2 \cdot x + 2 \cdot 3 \)
