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

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions

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