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Simple Equations Worksheet for Class 7 — Free Printable PDF

A simple equation is a mathematical statement of equality between two expressions that contains one variable (like x, y or n) raised to the power one. Solving the equation means finding the value of that variable which makes the left-hand side (LHS) equal to the right-hand side (RHS). This is the foundation of algebra in NCERT Class 7 Mathematics, Chapter 4 — Simple Equations, and it prepares students for linear equations in Class 8 and beyond.

The core idea is balance. Think of the equals sign as the pivot of a see-saw — whatever you do to one side, you must do to the other, otherwise the balance breaks. Class 7 students learn two closely related techniques: the balance method (adding, subtracting, multiplying or dividing the same number on both sides) and the transposition method (moving a term from one side to the other and changing its sign). Every worksheet on this page mixes one-step problems, two-step problems, and short word-problems so students get graded practice with an answer key.

Transposition — the quick rule

When you move a term across the equals sign:

  • a + becomes − (and vice-versa)
  • a × becomes ÷ (and vice-versa)

So `x + 5 = 12` becomes `x = 12 − 5 = 7`. And `3x = 21` becomes `x = 21 ÷ 3 = 7`. Always verify by substituting the answer back into the original equation — if LHS = RHS, your answer is correct.

Three fully worked examples

  • Example 1 — Solve `x + 7 = 12`. Transpose 7 to RHS: `x = 12 − 7`. So `x = 5`. Check: 5 + 7 = 12. ✓
  • Example 2 — Solve `3y = 21`. Divide both sides by 3: `y = 21 ÷ 3`. So `y = 7`. Check: 3 × 7 = 21. ✓
  • Example 3 — Solve `2x − 5 = 11`. Transpose −5 to RHS: `2x = 11 + 5 = 16`. Divide both sides by 2: `x = 16 ÷ 2`. So `x = 8`. Check: 2 × 8 − 5 = 16 − 5 = 11. ✓

Common mistakes to avoid

  • Forgetting to change the sign when transposing a term across `=`.
  • Doing an operation on only one side of the equation (breaks the balance).
  • Confusing variable × number with variable + number — write `3x` when you mean "three times x", not `x + 3`.
  • Skipping the verification step — always substitute your answer back.
  • In word problems, choosing the variable but not clearly writing "Let x = …" before setting up the equation.

The rule, simply

  • An equation has an equals sign and stays balanced — whatever you do to one side, do to the other.
  • The balance method: add, subtract, multiply or divide the same value on both sides.
  • Transposition: a term moved across the equals sign changes its sign (+ becomes −, × becomes ÷).
  • Always verify by substituting the value of the variable back into the original equation.
  • Read word problems twice: identify the unknown, choose a variable, write the equation, then solve.

Example questions

  1. Solve: x + 7 = 12Answer: Transpose 7 to RHS: x = 12 − 7 = 5. Check: 5 + 7 = 12 ✓
  2. Solve: 3y = 21Answer: Divide both sides by 3: y = 21 ÷ 3 = 7. Check: 3 × 7 = 21 ✓
  3. Solve: 2x − 5 = 11Answer: Transpose −5: 2x = 16. Divide by 2: x = 8. Check: 2×8 − 5 = 11 ✓
  4. Solve: (n/4) + 2 = 6Answer: Transpose 2: n/4 = 4. Multiply both sides by 4: n = 16. Check: 16/4 + 2 = 6 ✓
  5. Five more than thrice a number is 20. Find the number.Answer: Let the number be x. 3x + 5 = 20 → 3x = 15 → x = 5. Check: 3×5 + 5 = 20 ✓

Printable worksheets

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Class 7 Mathematics: Solving Simple Equations Practice Set

Step-by-step practice on solving simple equations for Class 7 — one-step and two-step problems using the balance method and transposition, with a full answer key.

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This worksheet will help students practice solving various simple equations and understanding their applications. It covers solving for variables and forming equations from given statements.

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FAQs

What is a simple equation in Class 7?
A simple equation is a statement of equality involving one variable (like x or y) where the highest power of the variable is one. Solving means finding the value of the variable that makes both sides equal.
Which NCERT chapter covers simple equations?
NCERT Class 7 Mathematics Chapter 4 — Simple Equations. These worksheets follow that syllabus and prepare students for linear equations in Class 8.
Is the answer key included?
Yes. Every printable worksheet on this page has a full answer key — open the worksheet and use the With answer key download.
Are these worksheets free to download?
Yes — all WorkbookWala printables are free. No sign-up required.
How is this different from Class 8 linear equations?
Class 7 simple equations focus on one-step and basic two-step problems with one variable. Class 8 extends this to linear equations in one variable with brackets, fractions, and more complex word problems.