Combine like terms to simplify pre-algebra expressions.

Let's solve each expression by combining like terms. Like terms are terms that have the same variable raised to the same power (e.g., $2r$ and $-4r$ are like terms).

We'll go through each expression one by one.

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1. $ 2r + 1 + (-4r) + 7 $

- Combine the $r$ terms: $2r - 4r = -2r$
- Combine the constants: $1 + 7 = 8$
- Answer: $-2r + 8$

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2. $ 3z + 2 + (-5z) + 6 $

- Combine the $z$ terms: $3z - 5z = -2z$
- Combine the constants: $2 + 6 = 8$
- Answer: $-2z + 8$

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3. $ -3z - z $

- Combine the $z$ terms: $-3z - z = -4z$
- Answer: $-4z$

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4. $ -4y - 4 + (-3) $

- The $y$ term is just $-4y$
- Constants: $-4 + (-3) = -7$
- Answer: $-4y - 7$

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5. $ -2k + (-4k) + 5 $

- Combine $k$ terms: $-2k - 4k = -6k$
- Constant: $+5$
- Answer: $-6k + 5$

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6. $ 4t + 2 + (-3t) + 6 $

- Combine $t$ terms: $4t - 3t = t$
- Constants: $2 + 6 = 8$
- Answer: $t + 8$

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7. $ 4z - (-3z) $

- Subtracting a negative is the same as adding: $4z + 3z = 7z$
- Answer: $7z$

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8. $ -2k - (-5) + 1 $

- $-(-5) = +5$, so: $-2k + 5 + 1$
- Constants: $5 + 1 = 6$
- Answer: $-2k + 6$

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9. $ -4q - (-8q) + 10 $

- $-(-8q) = +8q$, so: $-4q + 8q + 10$
- Combine $q$ terms: $-4q + 8q = 4q$
- Constant: $+10$
- Answer: $4q + 10$

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10. $ -4h + 3 + (-2h) + 3 $

- Combine $h$ terms: $-4h - 2h = -6h$
- Constants: $3 + 3 = 6$
- Answer: $-6h + 6$

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✔ Final Answers:

| Expression | Simplified |
|----------|------------|
| $2r + 1 + (-4r) + 7$ | $-2r + 8$ |
| $3z + 2 + (-5z) + 6$ | $-2z + 8$ |
| $-3z - z$ | $-4z$ |
| $-4y - 4 + (-3)$ | $-4y - 7$ |
| $-2k + (-4k) + 5$ | $-6k + 5$ |
| $4t + 2 + (-3t) + 6$ | $t + 8$ |
| $4z - (-3z)$ | $7z$ |
| $-2k - (-5) + 1$ | $-2k + 6$ |
| $-4q - (-8q) + 10$ | $4q + 10$ |
| $-4h + 3 + (-2h) + 3$ | $-6h + 6$ |

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🔍 Explanation:

To combine like terms:
1. Identify variables and constants.
2. Add or subtract coefficients of the same variable.
3. Keep the variable part unchanged.
4. Combine constant numbers separately.

This simplifies expressions into their most compact form while maintaining equivalence.

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