4. Which set of expressions below are not equivalent? A. $$ 8(3 x+7) $$ and $$ 8(3 x)+8(7) $$ B. $$ 3(8 x+7) $$ and $$ 11 x+10 $$ C. $$ 7(3 x+8) $$ and $$ 7 \cdot 3 x+7 \cdot 8 $$ D. $$ 3(7 x+8) $$ and $$ 21 x+24 $$

Question

UpStudy AI · Accepted Answer

Let's evaluate each pair of expressions to determine which set is **not equivalent**.

### **Option A**
$$ 8(3x + 7) \quad \text{and} \quad 8(3x) + 8(7) $$

Using the distributive property:
$$
8(3x + 7) = 8 \cdot 3x + 8 \cdot 7 = 24x + 56
$$
$$
8(3x) + 8(7) = 24x + 56
$$
**Equivalent**

---

### **Option B**
$$ 3(8x + 7) \quad \text{and} \quad 11x + 10 $$

Expanding the left expression:
$$
3(8x + 7) = 24x + 21
$$
Comparing to the right expression:
$$
24x + 21 \quad \text{vs.} \quad 11x + 10
$$
These are **not equivalent** because $$24x \neq 11x$$ and $$21 \neq 10$$.

---

### **Option C**
$$ 7(3x + 8) \quad \text{and} \quad 7 \cdot 3x + 7 \cdot 8 $$

Applying the distributive property:
$$
7(3x + 8) = 21x + 56
$$
$$
7 \cdot 3x + 7 \cdot 8 = 21x + 56
$$
**Equivalent**

---

### **Option D**
$$ 3(7x + 8) \quad \text{and} \quad 21x + 24 $$

Expanding the left expression:
$$
3(7x + 8) = 21x + 24
$$
Which matches the right expression.
**Equivalent**

---

**Conclusion:**  
Only **Option B** contains a pair of expressions that are **not equivalent**.

**Answer:**  
**B. $$ 3(8 x+7) $$ and $$ 11 x+10 $$**
**Option B** is not equivalent.

Which set of expressions below are not
equivalent?
A. and
B. and
C. and
D. and

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Solución

Option A

Option B

Option C

Option D

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