Solve Equations With Variables On Both Sides Worksheet - Free Printable

Let’s solve each equation step by step. We’ll follow the same method shown in the example: get all variable terms on one side and constants on the other, then solve for the variable.

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Problem 1: –5y + 35 = 2y

Step 1: Move all y-terms to one side. Subtract 2y from both sides:
–5y – 2y + 35 = 0 → –7y + 35 = 0

Step 2: Move constant to the other side. Subtract 35 from both sides:
–7y = –35

Step 3: Divide both sides by –7:
y = (–35)/(–7) = 5 ✔

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Problem 2: 27 + 8m = 5m

Step 1: Move m-terms together. Subtract 8m from both sides:
27 = 5m – 8m → 27 = –3m

Step 2: Divide both sides by –3:
m = 27 / (–3) = –9 ✔

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Problem 3: 5b = –3b + 24

Step 1: Add 3b to both sides to move all b-terms left:
5b + 3b = 24 → 8b = 24

Step 2: Divide by 8:
b = 24 / 8 = 3 ✔

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Problem 4: 7a – 3 = –23 – 3a

Step 1: Add 3a to both sides:
7a + 3a – 3 = –23 → 10a – 3 = –23

Step 2: Add 3 to both sides:
10a = –20

Step 3: Divide by 10:
a = –20 / 10 = –2 ✔

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Problem 5: –11h – 27 = 29 – 3h

Step 1: Add 3h to both sides:
–11h + 3h – 27 = 29 → –8h – 27 = 29

Step 2: Add 27 to both sides:
–8h = 56

Step 3: Divide by –8:
h = 56 / (–8) = –7 ✔

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Problem 6: 3z + 10 = –2z – 30

Step 1: Add 2z to both sides:
3z + 2z + 10 = –30 → 5z + 10 = –30

Step 2: Subtract 10 from both sides:
5z = –40

Step 3: Divide by 5:
z = –40 / 5 = –8 ✔

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Problem 7: 20 + 2u + 15 = 11u – 19

First, simplify left side: 20 + 15 = 35 → 35 + 2u = 11u – 19

Step 1: Subtract 2u from both sides:
35 = 9u – 19

Step 2: Add 19 to both sides:
54 = 9u

Step 3: Divide by 9:
u = 54 / 9 = 6 ✔

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Problem 8: 4 + 4c + 25 = 2c + 9

Simplify left side: 4 + 25 = 29 → 29 + 4c = 2c + 9

Step 1: Subtract 2c from both sides:
29 + 2c = 9

Step 2: Subtract 29 from both sides:
2c = –20

Step 3: Divide by 2:
c = –10 ✔

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Problem 9: –5r – 7 + 3r = 65 – 8r

Simplify left side: –5r + 3r = –2r → –2r – 7 = 65 – 8r

Step 1: Add 8r to both sides:
–2r + 8r – 7 = 65 → 6r – 7 = 65

Step 2: Add 7 to both sides:
6r = 72

Step 3: Divide by 6:
r = 72 / 6 = 12 ✔

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All answers match the provided answer key. Calculations verified.

Final Answer:
1. y = 5
2. m = –9
3. b = 3
4. a = –2
5. h = –7
6. z = –8
7. u = 6
8. c = –10
9. r = 12