Worksheet for combining like terms in algebra.

Let's solve the problem step by step. The task is to combine like terms in each algebraic expression, model the terms using visual representations (like algebra tiles), and then write the simplified expression.

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🔹 Understanding Like Terms:

- Like terms are terms that have the same variable raised to the same power.
- For example: $7x$ and $3x$ are like terms.
- Constants (numbers without variables) are also like terms.
- We can combine like terms by adding or subtracting their coefficients.

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We'll go through each row one at a time.

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✔ Row 1: Example

- Expression: $-2x + 3x + 5 - 1$
- Model: The image shows:
- Two negative $x$ tiles (–2x)
- Three positive $x$ tiles (+3x)
- Five positive unit tiles (+5)
- One negative unit tile (–1)
- Simplify:
- Combine $x$-terms: $-2x + 3x = x$
- Combine constants: $5 - 1 = 4$
- So, simplified expression: $x + 4$
- ✔ Matches the given answer.

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✔ Row 2: $7x + 3x$

- Expression: $7x + 3x$
- Model:
- Seven positive $x$ tiles
- Three positive $x$ tiles
- Total: $10x$
- Simplify:
- $7x + 3x = 10x$
- ✔ Simplified Expression: $10x$

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✔ Row 3: $-4x - x + 2$

- Expression: $-4x - x + 2$
- Model:
- Four negative $x$ tiles (–4x)
- One negative $x$ tile (–x)
- Two positive unit tiles (+2)
- Simplify:
- Combine $x$-terms: $-4x - x = -5x$
- Constant: $+2$
- So, simplified expression: $-5x + 2$
- ✔ Simplified Expression: $-5x + 2$

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✔ Row 4: $-6x + 5x - 3 + 2$

- Expression: $-6x + 5x - 3 + 2$
- Model:
- Six negative $x$ tiles (–6x)
- Five positive $x$ tiles (+5x)
- Three negative unit tiles (–3)
- Two positive unit tiles (+2)
- Simplify:
- $x$-terms: $-6x + 5x = -x$
- Constants: $-3 + 2 = -1$
- So, simplified expression: $-x - 1$
- ✔ Simplified Expression: $-x - 1$

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✔ Row 5: $3x + 2x - 7x$

- Expression: $3x + 2x - 7x$
- Model:
- Three positive $x$ tiles (+3x)
- Two positive $x$ tiles (+2x)
- Seven negative $x$ tiles (–7x)
- Simplify:
- Combine all $x$-terms: $3x + 2x - 7x = (5x) - 7x = -2x$
- ✔ Simplified Expression: $-2x$

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✔ Final Table with Answers:

| Expression | Model (Description) | Simplified Expression |
|------------------------|----------------------------------------------------------|------------------------|
| $-2x + 3x + 5 - 1$ | –2x, +3x, +5, –1 | $x + 4$ |
| $7x + 3x$ | 7 positive $x$, 3 positive $x$ | $10x$ |
| $-4x - x + 2$ | –4x, –x, +2 | $-5x + 2$ |
| $-6x + 5x - 3 + 2$ | –6x, +5x, –3, +2 | $-x - 1$ |
| $3x + 2x - 7x$ | +3x, +2x, –7x | $-2x$ |

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✔ Summary of Simplified Expressions:

1. $x + 4$
2. $10x$
3. $-5x + 2$
4. $-x - 1$
5. $-2x$

These are the final answers you would write in the "Simplified Expression" column.

Let me know if you'd like a visual sketch of the models!