Multi Step Equations Worksheet, Examples, And Practice - Free Printable

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

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1) $ 1 + 4x + 3 = 20 $

Step 1: Combine like terms on the left side:
$ 1 + 3 = 4 $, so:
$ 4x + 4 = 20 $

Step 2: Subtract 4 from both sides:
$ 4x = 16 $

Step 3: Divide both sides by 4:
$ x = 4 $

✔ Answer: $ x = 4 $

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2) $ x + 15 + x = 55 $

Step 1: Combine like terms:
$ x + x = 2x $, so:
$ 2x + 15 = 55 $

Step 2: Subtract 15 from both sides:
$ 2x = 40 $

Step 3: Divide by 2:
$ x = 20 $

✔ Answer: $ x = 20 $

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3) $ 46 = -3x - 5 + 6x $

Step 1: Combine like terms on the right side:
$ -3x + 6x = 3x $, so:
$ 46 = 3x - 5 $

Step 2: Add 5 to both sides:
$ 51 = 3x $

Step 3: Divide by 3:
$ x = 17 $

✔ Answer: $ x = 17 $

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4) $ -19 = 10 + 6x - 11 $

Step 1: Simplify the right side:
$ 10 - 11 = -1 $, so:
$ -19 = 6x - 1 $

Step 2: Add 1 to both sides:
$ -18 = 6x $

Step 3: Divide by 6:
$ x = -3 $

✔ Answer: $ x = -3 $

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5) $ 25 + 11x - 10 = 106 $

Step 1: Combine constants on the left:
$ 25 - 10 = 15 $, so:
$ 11x + 15 = 106 $

Step 2: Subtract 15 from both sides:
$ 11x = 91 $

Step 3: Divide by 11:
$ x = \frac{91}{11} \approx 8.27 $

But let's keep it as a fraction:
$ x = \frac{91}{11} $

✔ Answer: $ x = \frac{91}{11} $ (or $ 8\frac{3}{11} $)

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6) $ 10x + 3 + 4x = -25 $

Step 1: Combine like terms:
$ 10x + 4x = 14x $, so:
$ 14x + 3 = -25 $

Step 2: Subtract 3 from both sides:
$ 14x = -28 $

Step 3: Divide by 14:
$ x = -2 $

✔ Answer: $ x = -2 $

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7) $ -77 = -x + 1 - x $

Step 1: Combine like terms on the right:
$ -x - x = -2x $, so:
$ -77 = -2x + 1 $

Step 2: Subtract 1 from both sides:
$ -78 = -2x $

Step 3: Divide by -2:
$ x = 39 $

✔ Answer: $ x = 39 $

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8) $ -8 = 10 + 8x - 18 $

Step 1: Simplify the right side:
$ 10 - 18 = -8 $, so:
$ -8 = 8x - 8 $

Step 2: Add 8 to both sides:
$ 0 = 8x $

Step 3: Divide by 8:
$ x = 0 $

✔ Answer: $ x = 0 $

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✔ Final Answers:

1) $ x = 4 $
2) $ x = 20 $
3) $ x = 17 $
4) $ x = -3 $
5) $ x = \frac{91}{11} $
6) $ x = -2 $
7) $ x = 39 $
8) $ x = 0 $

Let me know if you'd like these explained in more detail or with visual steps!