Combining Like Terms - Kuta Software - Free Printable

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., $7k$ and $-6k$ are like terms, but $7k$ and $-6k^2$ are not).

We will simplify each expression step-by-step.

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1) $-6k + 7k$

Combine the coefficients of $k$:
$-6 + 7 = 1$
So:
$$
-6k + 7k = 1k = \boxed{k}
$$

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2) $12z - 8 - 12$

Combine the constant terms:
$-8 - 12 = -20$
So:
$$
12z - 8 - 12 = \boxed{12z - 20}
$$

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

Group like terms:
- Variables: $n + 9n = 10n$
- Constants: $-10 - 3 = -13$
So:
$$
n - 10 + 9n - 3 = \boxed{10n - 13}
$$

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4) $-4x - 10x$

Combine the coefficients:
$-4 - 10 = -14$
So:
$$
-4x - 10x = \boxed{-14x}
$$

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5) $-r - 10r$

Combine:
$-1 - 10 = -11$
So:
$$
-r - 10r = \boxed{-11r}
$$

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6) $-2t + 11 + 6t$

Group like terms:
- Variables: $-2t + 6t = 4t$
- Constant: $+11$
So:
$$
-2t + 11 + 6t = \boxed{4t + 11}
$$

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7) $11r - 12r$

Combine:
$11 - 12 = -1$
So:
$$
11r - 12r = \boxed{-r}
$$

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8) $-v + 12v$

Combine:
$-1 + 12 = 11$
So:
$$
-v + 12v = \boxed{11v}
$$

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9) $-8x - 11x$

Combine:
$-8 - 11 = -19$
So:
$$
-8x - 11x = \boxed{-19x}
$$

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10) $4p + 2p$

Combine:
$4 + 2 = 6$
So:
$$
4p + 2p = \boxed{6p}
$$

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11) $5n + 11n$

Combine:
$5 + 11 = 16$
So:
$$
5n + 11n = \boxed{16n}
$$

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12) $n + 4 - 9 - 5n$

Group like terms:
- Variables: $n - 5n = -4n$
- Constants: $4 - 9 = -5$
So:
$$
n + 4 - 9 - 5n = \boxed{-4n - 5}
$$

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13) $12r + 5 + 3r - 5$

Group like terms:
- Variables: $12r + 3r = 15r$
- Constants: $5 - 5 = 0$
So:
$$
12r + 5 + 3r - 5 = \boxed{15r}
$$

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14) $-5 + 9n + 6$

Group like terms:
- Constants: $-5 + 6 = 1$
- Variable: $9n$
So:
$$
-5 + 9n + 6 = \boxed{9n + 1}
$$

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✔ Final Answers:

1) $k$
2) $12z - 20$
3) $10n - 13$
4) $-14x$
5) $-11r$
6) $4t + 11$
7) $-r$
8) $11v$
9) $-19x$
10) $6p$
11) $16n$
12) $-4n - 5$
13) $15r$
14) $9n + 1$

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