Write a verbal expression of the algebraic expression. 2a + | Quizlet - Free Printable

The image presents a list of 22 verbal expressions that all describe the same algebraic expression:
$$
2a + 6
$$

The goal is to understand how these different phrases translate into the same mathematical expression, and to verify that they are all equivalent.

---

🔍 Step-by-step Analysis:

We are given a list of verbal phrases. Each one describes an operation involving:
- Multiplying a variable $ a $ by 2 (i.e., $ 2a $)
- Then adding 6 to it (i.e., $ + 6 $)

So, the core algebraic expression is:
$$
2a + 6
$$

Let’s go through each phrase and confirm whether it correctly represents $ 2a + 6 $. We’ll group them by meaning and explain the reasoning.

---

✔ All Phrases Represent $ 2a + 6 $

Here's the breakdown:

#### 🔹 Group 1: Direct multiplication + addition
These use simple phrasing like "times", "multiplied by".

1.) 2 times a plus 6 → $ 2a + 6 $ ✔
2.) 2 multiplied by a plus 6 → $ 2a + 6 $ ✔
3.) Twice the variable a plus 6 → $ 2a + 6 $ ✔
4.) The product of 2 and a plus 6 → $ 2a + 6 $ ✔
5.) 2 times a increased by 6 → $ 2a + 6 $ ✔
6.) 2 multiplied by a increased by 6 → $ 2a + 6 $ ✔
7.) Twice the variable a increased by 6 → $ 2a + 6 $ ✔
8.) The product of 2 and a increased by 6 → $ 2a + 6 $ ✔

> ✔ All of these clearly mean: multiply $ a $ by 2, then add 6.

---

#### 🔹 Group 2: Using "sum" or "total"

9.) The sum of 2 times a and 6 → $ 2a + 6 $ ✔
10.) The sum of 2 multiplied by a and 6 → $ 2a + 6 $ ✔
11.) The sum of twice the variable a and 6 → $ 2a + 6 $ ✔
12.) The total of 2 times a and 6 → $ 2a + 6 $ ✔
13.) The total of 2 multiplied by a and 6 → $ 2a + 6 $ ✔
14.) The total of twice the variable a and 6 → $ 2a + 6 $ ✔

> ✔ “Sum” and “total” indicate addition of two parts: $ 2a $ and $ 6 $

---

#### 🔹 Group 3: Using "more than"

15.) 6 more than 2 times a → $ 2a + 6 $ ✔
16.) 6 more than 2 multiplied by a → $ 2a + 6 $ ✔
17.) 6 more than twice the variable a → $ 2a + 6 $ ✔
18.) 6 more than the product of 2 and a → $ 2a + 6 $ ✔

> ⚠️ Note: “More than” reverses the order in English, but mathematically, “6 more than X” means $ X + 6 $, not $ 6 + X $.
> So “6 more than 2 times a” = $ 2a + 6 $ — correct.

---

#### 🔹 Group 4: Using "added to"

19.) 6 added to 2 times a → $ 2a + 6 $ ✔
20.) 6 added to 2 multiplied by a → $ 2a + 6 $ ✔
21.) 6 added to twice the variable a → $ 2a + 6 $ ✔
22.) 6 added to the product of 2 and a → $ 2a + 6 $ ✔

> ✔ “Added to” places the number being added at the end: “6 added to X” = $ X + 6 $

---

🧠 Key Concepts Explained

| Phrase Type | Meaning |
|-----------|--------|
| "Times" / "Multiplied by" | Multiplication: $ 2 \times a $ |
| "Twice" / "Double" | $ 2 \times a $ |
| "Product of" | Result of multiplication |
| "Plus" / "Increased by" / "Added to" | Addition |
| "Sum" / "Total" | Addition of two quantities |
| "More than" | Be careful! "X more than Y" = $ Y + X $, not $ X + Y $ |

---

✔ Final Answer:

All 22 verbal expressions listed are equivalent to the algebraic expression:

$$
\boxed{2a + 6}
$$

They represent the same mathematical idea using different words, demonstrating flexibility in translating algebra to language.

---

💡 Why This Matters:

In math, especially word problems, being able to recognize multiple ways to express the same operation helps with:
- Understanding problem statements
- Translating real-world situations into equations
- Avoiding misinterpretations due to wording

---

📌 Summary:

> The algebraic expression $ 2a + 6 $ can be expressed verbally in many ways, including:
> - "2 times a plus 6"
> - "Twice the variable a increased by 6"
> - "The sum of 2 times a and 6"
> - "6 more than twice a"
> - "6 added to the product of 2 and a"

✔ All 22 expressions are valid translations of $ \boxed{2a + 6} $.