Geometry - Skill - Solving Multi-Step Equations - Free Printable

Explanation:
We are solving 10 multi-step linear equations. Each equation has variables on both sides or constants mixed with variables — we need to isolate the variable (like *a*, *v*, *x*, etc.) by using inverse operations: addition/subtraction first, then multiplication/division.

Let’s solve each one step by step:

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1) $-2a + 7a = 10$
Combine like terms: $(-2a + 7a) = 5a$
So: $5a = 10$
Divide both sides by 5: $a = \frac{10}{5} = 2$

✔ Answer: $a = 2$

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2) $v - 7 + 3v = -15$
Combine like terms: $v + 3v = 4v$, so: $4v - 7 = -15$
Add 7 to both sides: $4v = -15 + 7 = -8$
Divide by 4: $v = \frac{-8}{4} = -2$

✔ Answer: $v = -2$

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3) $2 = -5x - 1 + 6x$
Combine like terms on right: $-5x + 6x = x$, so: $2 = x - 1$
Add 1 to both sides: $2 + 1 = x$ → $x = 3$

✔ Answer: $x = 3$

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4) $-6 = -3x - 3x$
Combine like terms: $-3x - 3x = -6x$, so: $-6 = -6x$
Divide both sides by -6: $x = \frac{-6}{-6} = 1$

✔ Answer: $x = 1$

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5) $4n - 7 + 6n = -7$
Combine like terms: $4n + 6n = 10n$, so: $10n - 7 = -7$
Add 7 to both sides: $10n = 0$
Divide by 10: $n = 0$

✔ Answer: $n = 0$

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6) $-24 = 5k - k$
Combine like terms: $5k - k = 4k$, so: $-24 = 4k$
Divide by 4: $k = \frac{-24}{4} = -6$

✔ Answer: $k = -6$

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7) $0 = 2x + 3x$
Combine: $2x + 3x = 5x$, so: $0 = 5x$
Divide by 5: $x = 0$

✔ Answer: $x = 0$

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8) $1 + 3p + 6p = -17$
Combine: $3p + 6p = 9p$, so: $1 + 9p = -17$
Subtract 1: $9p = -18$
Divide by 9: $p = \frac{-18}{9} = -2$

✔ Answer: $p = -2$

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9) $7n + 3n = -10$
Combine: $7n + 3n = 10n$, so: $10n = -10$
Divide: $n = \frac{-10}{10} = -1$

✔ Answer: $n = -1$

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10) $m + 5 - 7m = 11$
Combine like terms: $m - 7m = -6m$, so: $-6m + 5 = 11$
Subtract 5: $-6m = 6$
Divide by -6: $m = \frac{6}{-6} = -1$

✔ Answer: $m = -1$

Let me double-check a few tricky ones:

- #4: $-6 = -6x$ → $x = 1$ ✔
- #10: $m - 7m = -6m$, $-6m + 5 = 11$ → $-6m = 6$ → $m = -1$ ✔
- #5: $10n - 7 = -7$ → $10n = 0$ → $n = 0$ ✔

All correct.

Final Answer:
1) $a = 2$
2) $v = -2$
3) $x = 3$
4) $x = 1$
5) $n = 0$
6) $k = -6$
7) $x = 0$
8) $p = -2$
9) $n = -1$
10) $m = -1$