Simple Equations — One Operation
Simple Equations — One Operation. Practice questions to deepen understanding of simple equations with one operation. Online math practice with full solutions and step-by-step explanations.
Simple one-operation equations practice — 40 questions: addition, subtraction, multiplication, division. The golden rule (balance scale), inverse operations. Suitable for complete beginners.
Part A: What is an equation? (questions 1–6).
🤔 What is an equation?
Danny bought some sweets plus 3 chocolates. He has 7 items in total.
How many sweets did he buy?
This is the equation: x + 3 = 7
💡 Detailed Explanation:
An equation = a mathematical puzzle! 🎯
| x + 3 = 7 Think of it as a balance scale. Left side: x+3 | Right side: 7 x = 4 because 4 + 3 = 7 ✓ |
An equation = two equal sides, like a balance scale!
🔤 What is an unknown (variable)?
In the equation x + 5 = 12, what does x represent?
💡 Detailed Explanation:
x = a secret box! 📦
| x is "the unknown" Like a closed box with a number inside. Our goal: find what number is in the box! x + 5 = 12 → x = 7 because 7 + 5 = 12 |
🎯 What does it mean to "solve an equation"?
💡 Detailed Explanation:
Solving = revealing the secret! 🔓
| Find which number replaces x to make it true. x + 3 = 10: x=7 → 7+3=10 ✓ | x=5 → 5+3=8 ✗ Solution: x = 7 |
🔄 Important principle:
What is the inverse operation of addition?
💡 Detailed Explanation:
Inverse operations — the key! 🔑
| Addition ↔ Subtraction: +3 cancelled by −3 Multiplication ↔ Division: ×3 cancelled by ÷3 ⭐ Inverse operation undoes the original |
🔄 Important principle:
What is the inverse operation of multiplication?
💡 Detailed Explanation:
| 5 × 3 = 15 → 15 ÷ 3 = 5 ⭐ Division cancels multiplication! |
⭐ The golden rule:
What must you always do when solving an equation?
💡 Detailed Explanation:
The golden rule! ⭐
| ⭐ Golden Rule ⭐ x + 3 = 10 → subtract 3 from BOTH sides → x = 7 Same operation on both sides! |
✏️ Solve:
x + 5 = 12
💡 Detailed Explanation:
| x + 5 = 12 Subtract 5 from both sides: x = 12 − 5 = 7 Check: ✓ |
✏️ Solve:
x + 8 = 15
💡 Detailed Explanation:
| x + 8 = 15 Subtract 8: x = 15 − 8 = 7 Check: ✓ |
✏️ Solve:
x + 23 = 50
💡 Detailed Explanation:
| x + 23 = 50 Subtract 23: x = 50 − 23 = 27 Check: ✓ |
✏️ Solve:
15 = x + 6
💡 Detailed Explanation:
| 15 = x + 6 Same as x+6=15; subtract 6: x = 9 Check: ✓ |
✏️ Solve:
4 + x = 11
💡 Detailed Explanation:
| 4 + x = 11 Same as x+4=11; subtract 4: x = 7 Check: ✓ |
✏️ Solve:
x + 7 = 7
💡 Detailed Explanation:
| x + 7 = 7 Subtract 7: x = 7−7 = 0 (zero is valid!) Check: ✓ |
✏️ Solve:
x + 2.5 = 10
💡 Detailed Explanation:
| x + 2.5 = 10 Subtract 2.5: x = 10−2.5 = 7.5 Check: ✓ |
✏️ Solve:
x + 150 = 200
💡 Detailed Explanation:
| x + 150 = 200 Subtract 150: x = 200−150 = 50 Check: ✓ |
✏️ Solve:
x − 4 = 10
💡 Detailed Explanation:
| x − 4 = 10 Add 4 to both sides: x = 10+4 = 14 Check: ✓ |
✏️ Solve:
x − 7 = 20
💡 Detailed Explanation:
| x − 7 = 20 Add 7: x = 20+7 = 27 Check: ✓ |
✏️ Solve:
x − 5 = −2
💡 Detailed Explanation:
| x − 5 = −2 Add 5: x = −2+5 = 3 Check: ✓ |
✏️ Solve:
10 − x = 3
💡 Detailed Explanation:
| 10 − x = 3 10−x=3 → −x=−7 → x=7; check: 10−7=3 ✓ Check: ✓ |
✏️ Solve:
x − 35 = 65
💡 Detailed Explanation:
| x − 35 = 65 Add 35: x = 65+35 = 100 Check: ✓ |
✏️ Solve:
x − 12 = 0
💡 Detailed Explanation:
| x − 12 = 0 Add 12: x = 12. If x−a=0 then x=a Check: ✓ |
✏️ Solve:
x − 3.5 = 6.5
💡 Detailed Explanation:
| x − 3.5 = 6.5 Add 3.5: x = 6.5+3.5 = 10 Check: ✓ |
✏️ Solve:
25 = x − 8
💡 Detailed Explanation:
| 25 = x − 8 Same as x−8=25; add 8: x = 33 Check: ✓ |
✏️ Solve:
3x = 12
💡 Detailed Explanation:
| 3x = 12 Divide both sides by 3: x = 12÷3 = 4 Check: ✓ |
✏️ Solve:
2x = 18
💡 Detailed Explanation:
| 2x = 18 Divide by 2: x = 18÷2 = 9 Check: ✓ |
✏️ Solve:
5x = 35
💡 Detailed Explanation:
| 5x = 35 Divide by 5: x = 35÷5 = 7 Check: ✓ |
✏️ Solve:
4x = 10
💡 Detailed Explanation:
| 4x = 10 Divide by 4: x = 10÷4 = 2.5 (decimal is valid) Check: ✓ |
✏️ Solve:
7x = 63
💡 Detailed Explanation:
| 7x = 63 Divide by 7: x = 63÷7 = 9 Check: ✓ |
✏️ Solve:
24 = 6x
💡 Detailed Explanation:
| 24 = 6x Same as 6x=24; divide by 6: x = 4 Check: ✓ |
✏️ Solve:
8x = 0
💡 Detailed Explanation:
| 8x = 0 Divide by 8: x=0. If ax=0 (a≠0), x=0 Check: ✓ |
✏️ Solve:
12x = 60
💡 Detailed Explanation:
| 12x = 60 Divide by 12: x = 60÷12 = 5 Check: ✓ |
✏️ Solve:
x/3 = 5
💡 Detailed Explanation:
| x/3 = 5 Multiply both sides by 3: x = 5×3 = 15 Check: ✓ |
✏️ Solve:
x/4 = 7
💡 Detailed Explanation:
| x/4 = 7 Multiply by 4: x = 7×4 = 28 Check: ✓ |
✏️ Solve:
x/5 = 12
💡 Detailed Explanation:
| x/5 = 12 Multiply by 5: x = 12×5 = 60 Check: ✓ |
✏️ Solve:
x/2 = 3.5
💡 Detailed Explanation:
| x/2 = 3.5 Multiply by 2: x = 3.5×2 = 7 Check: ✓ |
✏️ Solve:
9 = x/6
💡 Detailed Explanation:
| 9 = x/6 Same as x/6=9; multiply by 6: x = 54 Check: ✓ |
✏️ Solve:
x/10 = 0
💡 Detailed Explanation:
| x/10 = 0 Multiply by 10: x=0. If x/a=0, x=0 Check: ✓ |
🤔 Question:
In the equation x + 7 = 15, what operation should you perform on both sides?
💡 Detailed Explanation:
| x + 7 = 15 To cancel +7, subtract 7 from both sides: x = 8 ⭐ Rule: +a → −a | −a → +a | ×a → ÷a | ÷a → ×a |
🤔 Question:
In the equation 4x = 20, what operation should you perform on both sides?
💡 Detailed Explanation:
| 4x = 20 x is multiplied by 4 → divide both sides by 4: x = 5 ⭐ Multiplication ↔ Division |
⚠️ Common mistake:
What is wrong with this solution?
x + 5 = 12
x = 12 + 5
x = 17
💡 Detailed Explanation:
The most common mistake! ⚠️
| ❌ Wrong: x = 12 + 5 = 17 → check: 17+5=22 ≠ 12 ✅ Correct: x = 12 − 5 = 7 → check: 7+5=12 ✓ ⭐ Always use the inverse operation! |
📋 Summary:
What is the general principle for solving simple equations?
💡 Detailed Explanation:
Summary of all rules! 📋
| Solving Simple Equations x+a=b → x=b−a x−a=b → x=b+a ax=b → x=b÷a x/a=b → x=b×a ⭐ Apply inverse operation to BOTH sides ⭐ Always check your answer! |