Practice worksheet featuring ten multi-step algebraic equations for students to solve.

Let's solve each of these multi-step equations step by step. I'll go through each one, showing the work and explaining the process.

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1) $-2a + 7a = 10$

Step 1: Combine like terms on the left side:
$(-2a + 7a) = 5a$

So:
$5a = 10$

Step 2: Divide both sides by 5:
$a = \frac{10}{5} = 2$

✔ Answer: $a = 2$

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2) $v - 7 + 3v = -15$

Step 1: Combine like terms:
$v + 3v = 4v$, so:
$4v - 7 = -15$

Step 2: Add 7 to both sides:
$4v = -15 + 7 = -8$

Step 3: Divide by 4:
$v = \frac{-8}{4} = -2$

✔ Answer: $v = -2$

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3) $2 = -5x - 1 + 6x$

Step 1: Combine like terms on the right:
$-5x + 6x = x$, so:
$2 = x - 1$

Step 2: Add 1 to both sides:
$2 + 1 = x \Rightarrow x = 3$

✔ Answer: $x = 3$

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4) $-6 = -3x - 3x$

Step 1: Combine like terms:
$-3x - 3x = -6x$

So:
$-6 = -6x$

Step 2: Divide both sides by -6:
$x = \frac{-6}{-6} = 1$

✔ Answer: $x = 1$

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5) $4n - 7 + 6n = -7$

Step 1: Combine like terms:
$4n + 6n = 10n$, so:
$10n - 7 = -7$

Step 2: Add 7 to both sides:
$10n = 0$

Step 3: Divide by 10:
$n = 0$

✔ Answer: $n = 0$

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6) $-24 = 5k - k$

Step 1: Combine like terms:
$5k - k = 4k$

So:
$-24 = 4k$

Step 2: Divide by 4:
$k = \frac{-24}{4} = -6$

✔ Answer: $k = -6$

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7) $0 = 2x + 3x$

Step 1: Combine like terms:
$2x + 3x = 5x$

So:
$0 = 5x$

Step 2: Divide by 5:
$x = 0$

✔ Answer: $x = 0$

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8) $1 + 3p + 6p = -17$

Step 1: Combine like terms:
$3p + 6p = 9p$

So:
$1 + 9p = -17$

Step 2: Subtract 1 from both sides:
$9p = -17 - 1 = -18$

Step 3: Divide by 9:
$p = \frac{-18}{9} = -2$

✔ Answer: $p = -2$

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9) $7n + 3n = -10$

Step 1: Combine like terms:
$7n + 3n = 10n$

So:
$10n = -10$

Step 2: Divide by 10:
$n = \frac{-10}{10} = -1$

✔ Answer: $n = -1$

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10) $m + 5 - 7m = 11$

Step 1: Combine like terms:
$m - 7m = -6m$

So:
$-6m + 5 = 11$

Step 2: Subtract 5 from both sides:
$-6m = 11 - 5 = 6$

Step 3: Divide by -6:
$m = \frac{6}{-6} = -1$

✔ Answer: $m = -1$

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✔ Final Answers:

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) $m = -1$

Let me know if you'd like a printed version or help checking your work!