Solving Multistep Equations worksheet - Free Printable

Let’s solve each equation step by step. I’ll go one at a time, showing all the work clearly so you can follow along.

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Problem (1):
4x – 2(5x + 2) = 26

Step 1: Distribute the -2 across the parentheses:
→ 4x – 10x – 4 = 26

Step 2: Combine like terms on the left:
→ -6x – 4 = 26

Step 3: Add 4 to both sides to isolate the variable term:
→ -6x = 30

Step 4: Divide both sides by -6:
→ x = -5

✔ Check: Plug x = -5 back in:
4(-5) – 2(5*(-5)+2) = -20 – 2(-25+2) = -20 – 2(-23) = -20 + 46 = 26 → Correct!

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Problem (2):
-36 = -5x + 4(2x – 3)

Step 1: Distribute the 4:
→ -36 = -5x + 8x – 12

Step 2: Combine like terms on the right:
→ -36 = 3x – 12

Step 3: Add 12 to both sides:
→ -24 = 3x

Step 4: Divide by 3:
→ x = -8

✔ Check: -5(-8) + 4(2*(-8)-3) = 40 + 4(-16-3) = 40 + 4(-19) = 40 - 76 = -36 → Correct!

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Problem (3):
-6x + 4(x + 2) = -4

Step 1: Distribute the 4:
→ -6x + 4x + 8 = -4

Step 2: Combine like terms:
→ -2x + 8 = -4

Step 3: Subtract 8 from both sides:
→ -2x = -12

Step 4: Divide by -2:
→ x = 6

✔ Check: -6(6) + 4(6+2) = -36 + 4(8) = -36 + 32 = -4 → Correct!

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Problem (4):
-20 = -7x + 4(2x – 2)

Step 1: Distribute the 4:
→ -20 = -7x + 8x – 8

Step 2: Combine like terms:
→ -20 = x – 8

Step 3: Add 8 to both sides:
→ -12 = x

So, x = -12

✔ Check: -7(-12) + 4(2*(-12)-2) = 84 + 4(-24-2) = 84 + 4(-26) = 84 - 104 = -20 → Correct!

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Problem (5):
42 = -3x + 7(x + 2)

Step 1: Distribute the 7:
→ 42 = -3x + 7x + 14

Step 2: Combine like terms:
→ 42 = 4x + 14

Step 3: Subtract 14 from both sides:
→ 28 = 4x

Step 4: Divide by 4:
→ x = 7

✔ Check: -3(7) + 7(7+2) = -21 + 7(9) = -21 + 63 = 42 → Correct!

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Problem (6):
2x + 4(2x – 2) = 42

Step 1: Distribute the 4:
→ 2x + 8x – 8 = 42

Step 2: Combine like terms:
→ 10x – 8 = 42

Step 3: Add 8 to both sides:
→ 10x = 50

Step 4: Divide by 10:
→ x = 5

✔ Check: 2(5) + 4(2*5 - 2) = 10 + 4(10-2) = 10 + 4(8) = 10 + 32 = 42 → Correct!

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Problem (7):
26 = 2x – 2(4x + 2)

Step 1: Distribute the -2:
→ 26 = 2x – 8x – 4

Step 2: Combine like terms:
→ 26 = -6x – 4

Step 3: Add 4 to both sides:
→ 30 = -6x

Step 4: Divide by -6:
→ x = -5

✔ Check: 2(-5) – 2(4*(-5)+2) = -10 – 2(-20+2) = -10 – 2(-18) = -10 + 36 = 26 → Correct!

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Problem (8):
28 = 2x + 3(2x – 4)

Step 1: Distribute the 3:
→ 28 = 2x + 6x – 12

Step 2: Combine like terms:
→ 28 = 8x – 12

Step 3: Add 12 to both sides:
→ 40 = 8x

Step 4: Divide by 8:
→ x = 5

✔ Check: 2(5) + 3(2*5 - 4) = 10 + 3(10-4) = 10 + 3(6) = 10 + 18 = 28 → Correct!

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Problem (9):
-15 = 3x + 6(-x + 2)

Step 1: Distribute the 6:
→ -15 = 3x – 6x + 12

Step 2: Combine like terms:
→ -15 = -3x + 12

Step 3: Subtract 12 from both sides:
→ -27 = -3x

Step 4: Divide by -3:
→ x = 9

✔ Check: 3(9) + 6(-9 + 2) = 27 + 6(-7) = 27 - 42 = -15 → Correct!

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Problem (10):
-2x + 2(-x – 2) = -24

Step 1: Distribute the 2:
→ -2x – 2x – 4 = -24

Step 2: Combine like terms:
→ -4x – 4 = -24

Step 3: Add 4 to both sides:
→ -4x = -20

Step 4: Divide by -4:
→ x = 5

✔ Check: -2(5) + 2(-5 - 2) = -10 + 2(-7) = -10 -14 = -24 → Correct!

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Final Answer:
(1) x = -5
(2) x = -8
(3) x = 6
(4) x = -12
(5) x = 7
(6) x = 5
(7) x = -5
(8) x = 5
(9) x = 9
(10) x = 5