3.1 Expressions and Equations worksheet - Free Printable

Let's solve this step by step using the given equation and the word bank.

The equation is:

3x + 10 = 22

We are to label each part using the words from the Word Bank:
- coefficient
- constant
- equation
- expression
- variable

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Step 1: Identify the parts of the equation

#### 1. The entire statement: 3x + 10 = 22
- This is a complete equation because it has an equal sign (=) and states that two expressions are equal.
- So, the entire line (the whole thing) should be labeled as: equation

#### 2. The left side: 3x + 10
- This is a mathematical expression (a combination of numbers, variables, and operations).
- It does not have an equals sign, so it’s not an equation by itself.
- So, the left side (under the first bracket) is: expression

#### 3. The right side: 22
- This is a number, which is a constant (a fixed value).
- But note: in the context of the full equation, 22 is also part of the equation, but the arrow points specifically to 22, so we label it as a constant.

Wait — actually, look at the diagram:

- There are three arrows pointing to different parts:
- One to 3
- One to x
- One to 10
- And one to 22
- Plus two brackets:
- One under 3x + 10 → that’s the left side
- One under the whole equation → entire thing

So let's break it down based on the arrows and brackets:

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Step 2: Match each part with the correct term

#### Arrow 1: Points to 3
- This is the number multiplied by the variable x
- That is called the coefficient
- ✔ Coefficient

#### Arrow 2: Points to x
- This is the letter representing an unknown value
- That is the variable
- ✔ Variable

#### Arrow 3: Points to 10
- This is a number that does not change and is not attached to a variable
- That is a constant
- ✔ Constant

#### Arrow 4: Points to 22
- This is also a number without a variable
- So, another constant
- ✔ Constant

But wait — both 10 and 22 are constants? Yes! Constants are just fixed numbers.

But the Word Bank only has one "constant" — but we can use it more than once if needed. The instruction says “use the words from the Word Bank”, not “use each word once”.

So yes, we can use constant for both 10 and 22.

However, let's double-check: is 22 considered a constant?

Yes — in this equation, 22 is a constant value.

So:
- 10 → constant
- 22 → constant

Now, the brackets:

#### Bracket 1: Under 3x + 10
- This is a mathematical expression (a combination of terms)
- So, label this as: expression

#### Bracket 2: Under the entire equation: 3x + 10 = 22
- This is an equation (because it has an equal sign)
- So, label this as: equation

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Final Answer:

Let’s fill in the blanks:

```
[coefficient] [variable] [constant]
↓ ↓ ↓
3x + 10 = 22
┌─────────┐
│ expression │
└─────────┘
┌───────────────────────┐
│ equation │
└───────────────────────┘
```

Wait — there’s a second blank under the big bracket (the whole equation), so we need to label that too.

Looking back at the image:

- There are five gray boxes:
1. Above 3 → coefficient
2. Above x → variable
3. Above 10 → constant
4. Above 22 → constant
5. Below the small bracket (under 3x+10) → expression
6. Below the large bracket (under whole equation) → equation

But there are only five gray boxes shown in the image — but six labels?

Wait, count them:

In the image:
- Three small boxes above: pointing to 3, x, and 10/22?
Wait — no:

Actually, looking carefully:

- Two arrows pointing to 3 and x
- One arrow pointing to 10 and 22 (but it splits into two lines, pointing to both 10 and 22)
- Then a bracket under 3x + 10
- Then a larger bracket under the whole equation

And five gray boxes:

1. First box → points to 3
2. Second box → points to x
3. Third box → points to 10 and 22? Wait, it has two arrows coming from it — one to 10 and one to 22?

Wait — the third box has two arrows going to 10 and 22 — so it's labeling both as the same thing.

That suggests the third box is meant to be constant, since both 10 and 22 are constants.

Then:
- Fourth box → under the expression bracket (3x + 10)
- Fifth box → under the equation bracket (whole thing)

So total of five boxes.

---

Correct labeling:

| Box | Label |
|-----|-------|
| 1 (→ 3) | coefficient |
| 2 (→ x) | variable |
| 3 (→ 10 and 22) | constant |
| 4 (under 3x+10) | expression |
| 5 (under whole equation) | equation |

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Final Answer:

Fill in the boxes:

1. coefficient
2. variable
3. constant
4. expression
5. equation

---

✔ Answer Summary:

- 3 → coefficient
- x → variable
- 10 and 22 → constant
- 3x + 10 → expression
- 3x + 10 = 22 → equation

This matches all terms in the Word Bank and correctly identifies each part.