Equations & Inequalities - Free Printable

You’ve uploaded an image titled “Two-step Equations”, and it lists 8 equations labeled a through h. The instruction says “Expand:”, but in the context of two-step equations, this likely means “Solve each equation for the variable.”

Let’s solve each one step-by-step.

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a) 6p – 2 = 52

Step 1: Add 2 to both sides
→ 6p = 54

Step 2: Divide both sides by 6
→ p = 9

✔ Answer: p = 9

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b) 6y + 9 = 21

Step 1: Subtract 9 from both sides
→ 6y = 12

Step 2: Divide both sides by 6
→ y = 2

✔ Answer: y = 2

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c) 9d + 1 = 19

Step 1: Subtract 1 from both sides
→ 9d = 18

Step 2: Divide both sides by 9
→ d = 2

✔ Answer: d = 2

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d) 2x – 5 = 19

Step 1: Add 5 to both sides
→ 2x = 24

Step 2: Divide both sides by 2
→ x = 12

✔ Answer: x = 12

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e) 6a – 1 = 41

Step 1: Add 1 to both sides
→ 6a = 42

Step 2: Divide both sides by 6
→ a = 7

✔ Answer: a = 7

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f) 4 = 4 + 4x

Step 1: Subtract 4 from both sides
→ 0 = 4x

Step 2: Divide both sides by 4
→ x = 0

✔ Answer: x = 0

*(Note: This is a trickier one — many students might miss that subtracting 4 from both sides gives 0 = 4x.)*

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g) 10 = 2m + 10

Step 1: Subtract 10 from both sides
→ 0 = 2m

Step 2: Divide both sides by 2
→ m = 0

✔ Answer: m = 0

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h) 3 + 8y = 99

Step 1: Subtract 3 from both sides
→ 8y = 96

Step 2: Divide both sides by 8
→ y = 12

✔ Answer: y = 12

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## ✔ Final Answers:

a) p = 9
b) y = 2
c) d = 2
d) x = 12
e) a = 7
f) x = 0
g) m = 0
h) y = 12

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## 💡 Explanation Summary:

These are called two-step equations because they require two inverse operations to isolate the variable:

1. First, undo addition or subtraction (using the opposite operation).
2. Then, undo multiplication or division (again, using the opposite operation).

Always perform the same operation on both sides to keep the equation balanced.

Let me know if you’d like to see these solved with diagrams or visual steps!