Simplifying Algebraic Expressions with Two Variables and Four - Free Printable

Let's solve each expression on the worksheet by combining like terms. Like terms are terms that have the same variable raised to the same power (e.g., $8x$ and $-4x$ both have the variable $x$).

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1. $8x + 4x$

- Both terms have $x$, so combine coefficients:
$$
8x + 4x = (8 + 4)x = 12x
$$
✔ Answer: $12x$

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2. $5x - (-4x)$

- Subtracting a negative is the same as adding:
$$
5x - (-4x) = 5x + 4x = 9x
$$
✔ Answer: $9x$

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3. $2 + x - 8x + 4$

- Combine constant terms: $2 + 4 = 6$
- Combine $x$ terms: $x - 8x = -7x$
$$
2 + x - 8x + 4 = 6 - 7x
$$
✔ Answer: $6 - 7x$

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4. $x + 6x + x + x$

- All terms are $x$: $1x + 6x + 1x + 1x = (1+6+1+1)x = 9x$
✔ Answer: $9x$

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5. $-10x + 5x$

- Combine coefficients: $-10 + 5 = -5$
$$
-10x + 5x = -5x
$$
✔ Answer: $-5x$

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6. $x + x + x + x + x$

- Five $x$'s: $5x$
✔ Answer: $5x$

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7. $-8x + (-4x)$

- Adding two negatives: $-8x - 4x = -12x$
✔ Answer: $-12x$

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8. $-9x - 6 + 4x$

- Combine $x$ terms: $-9x + 4x = -5x$
- Constant term: $-6$
$$
-9x - 6 + 4x = -5x - 6
$$
✔ Answer: $-5x - 6$

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9. $-x + 8 + (-10x)$

- Combine $x$ terms: $-x - 10x = -11x$
- Constant: $+8$
$$
-x + 8 - 10x = -11x + 8
$$
✔ Answer: $-11x + 8$

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10. $7x - 6x - 4 + 5x$

- Combine $x$ terms: $7x - 6x + 5x = (7 - 6 + 5)x = 6x$
- Constant: $-4$
$$
7x - 6x - 4 + 5x = 6x - 4
$$
✔ Answer: $6x - 4$

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✔ Final Answers:

1. $12x$
2. $9x$
3. $6 - 7x$
4. $9x$
5. $-5x$
6. $5x$
7. $-12x$
8. $-5x - 6$
9. $-11x + 8$
10. $6x - 4$

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