Solve algebraic equations with this printable worksheet from Learners' Planet.

Let's solve each of the algebraic equations step by step. The goal is to isolate the variable on one side of the equation.

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1) $-10 + v = -2$

Add 10 to both sides:
$v = -2 + 10 = 8$
✔ Answer: $v = 8$

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2) $19 + x = 14$

Subtract 19 from both sides:
$x = 14 - 19 = -5$
✔ Answer: $x = -5$

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3) $x - 2 = -20$

Add 2 to both sides:
$x = -20 + 2 = -18$
✔ Answer: $x = -18$

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4) $a - 14 = -3$

Add 14 to both sides:
$a = -3 + 14 = 11$
✔ Answer: $a = 11$

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5) $k - 6 = 1$

Add 6 to both sides:
$k = 1 + 6 = 7$
✔ Answer: $k = 7$

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6) $-6 + p = -12$

Add 6 to both sides:
$p = -12 + 6 = -6$
✔ Answer: $p = -6$

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7) $x + 15 = -4$

Subtract 15 from both sides:
$x = -4 - 15 = -19$
✔ Answer: $x = -19$

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8) $n - 3 = 7$

Add 3 to both sides:
$n = 7 + 3 = 10$
✔ Answer: $n = 10$

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9) $m - 18 = -12$

Add 18 to both sides:
$m = -12 + 18 = 6$
✔ Answer: $m = 6$

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10) $x + 10 = -9$

Subtract 10 from both sides:
$x = -9 - 10 = -19$
✔ Answer: $x = -19$

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11) $r - 11 = -18$

Add 11 to both sides:
$r = -18 + 11 = -7$
✔ Answer: $r = -7$

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12) $n + 10 = 19$

Subtract 10 from both sides:
$n = 19 - 10 = 9$
✔ Answer: $n = 9$

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13) $b - 1 = 4$

Add 1 to both sides:
$b = 4 + 1 = 5$
✔ Answer: $b = 5$

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14) $v - 19 = -26$

Add 19 to both sides:
$v = -26 + 19 = -7$
✔ Answer: $v = -7$

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15) $x - 7 = -27$

Add 7 to both sides:
$x = -27 + 7 = -20$
✔ Answer: $x = -20$

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16) $n + 14 = 31$

Subtract 14 from both sides:
$n = 31 - 14 = 17$
✔ Answer: $n = 17$

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17) $a + 15 = 20$

Subtract 15 from both sides:
$a = 20 - 15 = 5$
✔ Answer: $a = 5$

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18) $k - 5 = -13$

Add 5 to both sides:
$k = -13 + 5 = -8$
✔ Answer: $k = -8$

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19) $x - 3 = 14$

Add 3 to both sides:
$x = 14 + 3 = 17$
✔ Answer: $x = 17$

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20) $x - 17 = 3$

Add 17 to both sides:
$x = 3 + 17 = 20$
✔ Answer: $x = 20$

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21) $-10 + n = 39$

Add 10 to both sides:
$n = 39 + 10 = 49$
✔ Answer: $n = 49$

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22) $p - 23 = -12$

Add 23 to both sides:
$p = -12 + 23 = 11$
✔ Answer: $p = 11$

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23) $34 + k = 64$

Subtract 34 from both sides:
$k = 64 - 34 = 30$
✔ Answer: $k = 30$

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24) $x + 35 = 2$

Subtract 35 from both sides:
$x = 2 - 35 = -33$
✔ Answer: $x = -33$

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25) $n - 9 = 9$

Add 9 to both sides:
$n = 9 + 9 = 18$
✔ Answer: $n = 18$

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26) $-4 + m = -5$

Add 4 to both sides:
$m = -5 + 4 = -1$
✔ Answer: $m = -1$

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27) $r + 40 = 21$

Subtract 40 from both sides:
$r = 21 - 40 = -19$
✔ Answer: $r = -19$

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28) $x - 27 = -21$

Add 27 to both sides:
$x = -21 + 27 = 6$
✔ Answer: $x = 6$

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29) $n - 30 = -43$

Add 30 to both sides:
$n = -43 + 30 = -13$
✔ Answer: $n = -13$

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30) $h - 42 = -73$

Add 42 to both sides:
$h = -73 + 42 = -31$
✔ Answer: $h = -31$

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31) $v + 2 = -48$

Subtract 2 from both sides:
$v = -48 - 2 = -50$
✔ Answer: $v = -50$

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32) $x + 11 = -14$

Subtract 11 from both sides:
$x = -14 - 11 = -25$
✔ Answer: $x = -25$

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33) $a - 24 = 15$

Add 24 to both sides:
$a = 15 + 24 = 39$
✔ Answer: $a = 39$

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34) $x - 33 = -76$

Add 33 to both sides:
$x = -76 + 33 = -43$
✔ Answer: $x = -43$

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35) $k + 37 = 0$

Subtract 37 from both sides:
$k = 0 - 37 = -37$
✔ Answer: $k = -37$

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36) $p + 8 = 54$

Subtract 8 from both sides:
$p = 54 - 8 = 46$
✔ Answer: $p = 46$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $v = 8$ |
| 2 | $x = -5$ |
| 3 | $x = -18$ |
| 4 | $a = 11$ |
| 5 | $k = 7$ |
| 6 | $p = -6$ |
| 7 | $x = -19$ |
| 8 | $n = 10$ |
| 9 | $m = 6$ |
| 10 | $x = -19$ |
| 11 | $r = -7$ |
| 12 | $n = 9$ |
| 13 | $b = 5$ |
| 14 | $v = -7$ |
| 15 | $x = -20$ |
| 16 | $n = 17$ |
| 17 | $a = 5$ |
| 18 | $k = -8$ |
| 19 | $x = 17$ |
| 20 | $x = 20$ |
| 21 | $n = 49$ |
| 22 | $p = 11$ |
| 23 | $k = 30$ |
| 24 | $x = -33$ |
| 25 | $n = 18$ |
| 26 | $m = -1$ |
| 27 | $r = -19$ |
| 28 | $x = 6$ |
| 29 | $n = -13$ |
| 30 | $h = -31$ |
| 31 | $v = -50$ |
| 32 | $x = -25$ |
| 33 | $a = 39$ |
| 34 | $x = -43$ |
| 35 | $k = -37$ |
| 36 | $p = 46$ |

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🔍 Explanation of Method:

All these are linear equations in one variable. To solve them:
1. Use inverse operations (addition/subtraction) to isolate the variable.
2. Move constants to the other side by performing the opposite operation.
3. Simplify and find the value.

For example:
If $x + a = b$, then $x = b - a$.
If $x - a = b$, then $x = b + a$.

This method applies consistently across all problems.

Let me know if you'd like this in a printable format or with steps shown for each!