Algebra worksheet with multi-step equations for practice.

Here is the step-by-step solution to all 18 multi-step equations from the Kuta Software worksheet. Each equation is solved using algebraic techniques: combining like terms, distributing, moving variables to one side, and isolating the variable.

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1) -20 = -4x - 6x

Combine like terms on right:
-20 = -10x

Divide both sides by -10:
x = (-20)/(-10) = 2

✔ Answer: x = 2

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2) 6 = 1 - 2n + 5

Simplify right side:
6 = 6 - 2n

Subtract 6 from both sides:
0 = -2n

Divide by -2:
n = 0

✔ Answer: n = 0

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3) 8x - 2 = -9 + 7x

Move variables to left, constants to right:
8x - 7x = -9 + 2

x = -7

✔ Answer: x = -7

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4) a + 5 = -5a + 5

Move variables to left, constants to right:
a + 5a = 5 - 5

6a = 0

a = 0

✔ Answer: a = 0

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5) 4m - 4 = 4m

Subtract 4m from both sides:
-4 = 0 → Contradiction

No solution.

✔ Answer: No solution

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6) p - 1 = 5p + 3p - 8

Simplify right:
p - 1 = 8p - 8

Move variables to right, constants to left:
-1 + 8 = 8p - p

7 = 7p

p = 1

✔ Answer: p = 1

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7) 5p - 14 = 8p + 4

Move variables to right, constants to left:
-14 - 4 = 8p - 5p

-18 = 3p

p = -6

✔ Answer: p = -6

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8) p - 4 = -9 + p

Subtract p from both sides:
-4 = -9 → Contradiction

No solution.

✔ Answer: No solution

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9) -8 = -(x + 4)

Distribute negative sign:
-8 = -x - 4

Add x to both sides:
x - 8 = -4

Add 8 to both sides:
x = 4

✔ Answer: x = 4

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10) 12 = -4(-6x - 3)

Distribute -4:
12 = 24x + 12

Subtract 12 from both sides:
0 = 24x

x = 0

✔ Answer: x = 0

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11) 14 = -(p - 8)

Distribute negative:
14 = -p + 8

Subtract 8:
6 = -p

Multiply by -1:
p = -6

✔ Answer: p = -6

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12) -(7 - 4x) = 9

Distribute negative:
-7 + 4x = 9

Add 7:
4x = 16

x = 4

✔ Answer: x = 4

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13) -18 - 6k = 6(1 + 3k)

Distribute right:
-18 - 6k = 6 + 18k

Move variables to right, constants to left:
-18 - 6 = 18k + 6k

-24 = 24k

k = -1

✔ Answer: k = -1

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14) 5n + 34 = -2(1 - 7n)

Distribute right:
5n + 34 = -2 + 14n

Move variables to right, constants to left:
34 + 2 = 14n - 5n

36 = 9n

n = 4

✔ Answer: n = 4

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15) 2(4x - 3) - 8 = 4 + 2x

Distribute:
8x - 6 - 8 = 4 + 2x

Simplify left:
8x - 14 = 4 + 2x

Move variables to left, constants to right:
8x - 2x = 4 + 14

6x = 18

x = 3

✔ Answer: x = 3

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16) 3n - 5 = -8(6 + 5n)

Distribute right:
3n - 5 = -48 - 40n

Move variables to left, constants to right:
3n + 40n = -48 + 5

43n = -43

n = -1

✔ Answer: n = -1

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17) -(1 + 7x) - 6(-7 - x) = 36

Distribute both terms:
-1 - 7x + 42 + 6x = 36

Combine like terms:
(-7x + 6x) + (-1 + 42) = 36

-x + 41 = 36

Subtract 41:
-x = -5

Multiply by -1:
x = 5

✔ Answer: x = 5

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18) -3(4x + 3) + 4(6x + 1) = 43

Distribute:
-12x - 9 + 24x + 4 = 43

Combine like terms:
(-12x + 24x) + (-9 + 4) = 43

12x - 5 = 43

Add 5:
12x = 48

x = 4

✔ Answer: x = 4

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## ✔ Final Answers:

1) x = 2
2) n = 0
3) x = -7
4) a = 0
5) No solution
6) p = 1
7) p = -6
8) No solution
9) x = 4
10) x = 0
11) p = -6
12) x = 4
13) k = -1
14) n = 4
15) x = 3
16) n = -1
17) x = 5
18) x = 4

Let me know if you’d like to see any step explained in more detail!