3. Are the following expressions equivalent? Justity your answer by showing your work $$ \begin{array}{l} ext { a) } 5 x+2 \quad 4 x+1+x+2 \quad ext { and } \ ext { Justify your answer. }\end{array} l $$

Question

3. Are the following expressions equivalent? Justity your answer by showing your work $$ \begin{array}{l}	ext { a) } 5 x+2 \quad 4 x+1+x+2 \quad 	ext { and } \ 	ext { Justify your answer. }\end{array} l $$

UpStudy AI · Accepted Answer

Certainly! Let's examine whether the two expressions are equivalent by simplifying each and comparing the results.

### **a) Expressions:**

1. **First Expression:**  
   $$ 5x + 2 $$

2. **Second Expression:**  
   $$ 4x + 1 + x + 2 $$

### **Simplifying the Second Expression:**

Let's combine like terms in the second expression.

$$
\begin{align*}
4x + 1 + x + 2 &= (4x + x) + (1 + 2) \
&= 5x + 3
\end{align*}
$$

### **Comparing Both Expressions:**

- **First Expression:** $$ 5x + 2 $$
- **Simplified Second Expression:** $$ 5x + 3 $$

### **Conclusion:**

Since $$ 5x + 2 $$ is **not equal** to $$ 5x + 3 $$ (the constant terms differ), the two expressions are **not equivalent**.

### **Final Answer:**

**No, the expressions are not equivalent.**

$$
\begin{align*}
5x + 2 &\neq 4x + 1 + x + 2 \
5x + 2 &\neq 5x + 3
\end{align*}
$$
The expressions $$5x + 2$$ and $$4x + 1 + x + 2$$ are not equivalent because simplifying the second expression gives $$5x + 3$$, which is different from the first expression.

Are the following expressions equivalent? Justity your answer by showing your work

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