Solving equations – Grade 7
Solve linear equations: transform both sides, isolate x and check by substituting into the original equation. Create a free worksheet or try an online test.
🎯 What you will learn
- ✓Apply the same operation to both sides
- ✓Check in the original equation
💡 How it works
An equation requires two expressions to have the same value. Find the x that makes the equality true.
How it works
💡 Add or subtract the same quantity on both sides. Multiply or divide both sides by the same nonzero number.
In 4x − 7 = 21, first undo −7 by adding 7 to both sides. That leaves 4x = 28. Divide the entire left and right sides by 4. Write each step on a new line so every equality stays valid.
If x appears on both sides, subtract an x term from both sides first. This is more precise than “move it across”. Check in the original equation so a transformation error cannot hide.
🧩 See the method
✍️ Worked examples
Worked examples 1
4x − 7 = 21
- 1.Add 7 to both sides: 4x = 28.
- 2.Divide both sides by 4: x = 7.
- 3.Check: 4 × 7 − 7 = 28 − 7 = 21.
✓ x = 7
Worked examples 2
5x + 2 = 2x + 17
- 1.Subtract 2x from both sides: 3x + 2 = 17.
- 2.Subtract 2, then divide by 3 on both sides: 3x = 15; x = 5.
- 3.Check: left 5 × 5 + 2 = 27; right 2 × 5 + 17 = 27.
✓ x = 5
⚠️ Common mistakes
- • Changing only one side. Each transformation must preserve equality.
- • Subtracting 4 in 4x = 28. Since 4x means 4 × x, the inverse is division.
📝 Try it yourself
1.
3x + 4 = 19
Show answer
x = 5
2.
5x − 6 = 24
Show answer
x = 6
3.
2x + 9 = 3
Show answer
x = −3
4.
4x + 1 = 2x + 13
Show answer
x = 6
5.
7x − 5 = 3x + 11
Show answer
x = 4
6.
6x = 15
Show answer
x = 2,5
Create matching questions
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FAQ
Must x be a positive whole number?
No. 2x + 9 = 3 gives x = −3; 6x = 15 gives x = 2.5. Respect any specified number domain.
What does 0x = 5 mean?
There is no solution because zero times any number is zero. For 0x = 0, every number in the allowed domain works.