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Tamil Nadu (TNBSE)Class 7 Mathematics★ 6-10 marks in the TN Class 7 Term 1 exam through expression simplification and equation solving

Algebra (Term 1) - Expressions and Equations

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 1 Chapter 3, Algebra. Algebraic expressions and their terms, factors and coefficients, like and unlike terms, addition and subtraction of expressions, evaluating expressions, and solving simple linear equations and word problems, with worked examples, exercises and quick revision.

⏱ 15 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Identify terms, factors and coefficients
2Distinguish like and unlike terms
3Add and subtract algebraic expressions
4Evaluate expressions by substitution
5Solve simple linear equations and word problems

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Why this chapter matters

Algebraic expressions and simple equations are the gateway to all higher algebra. Identifying terms and coefficients, combining like terms and solving equations are directly tested in the TN Class 7 Term 1 exam.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Class 6 — Introduction to Algebra

Variables and expressions.

Algebra (Expressions and Equations) — Class 7 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 7 Mathematics, Term 1 — Chapter 3. Building, simplifying and solving with algebraic expressions.

1. About this chapter

This chapter covers algebraic expressions — their terms, factors and coefficients, like and unlike terms, addition and subtraction of expressions, evaluating expressions, and solving simple linear equations and word problems.

2. Expressions, terms and coefficients

A variable is a letter (x, y …) that stands for a number; a constant has a fixed value.
An algebraic expression is built from variables and constants, e.g. 3x + 5.
A term is a part separated by + or − (in 3x + 5, the terms are 3x and 5); the numerical factor of a term is its coefficient (the coefficient of x in 3x is 3).
Like terms have the same variable part (5x and 2x); unlike terms do not (5x and 2y).

3. Adding and subtracting expressions

Add or subtract only like terms by adding/subtracting their coefficients.
Example: (3x + 5) + (4x − 2) = (3x + 4x) + (5 − 2) = 7x + 3.

4. Evaluating and solving equations

Evaluating: substitute the value of the variable. If x = 4, then 3x + 5 = 3(4) + 5 = 17.
An equation says two expressions are equal (e.g. x + 7 = 12). Solve by doing the same operation on both sides to isolate the variable.
Example: x + 7 = 12 → x = 12 − 7 → x = 5.

5. Worked examples

Example 1. Simplify 6a + 3b − 2a + b. = (6a − 2a) + (3b + b) = 4a + 4b.

Example 2. Solve 3x − 4 = 11. 3x = 11 + 4 = 15 → x = 15 ÷ 3 = 5.

Example 3. A number increased by 8 is 20. Find the number. x + 8 = 20 → x = 12.

6. Exercises (Samacheer Kalvi)

Write the terms and coefficients of 7x − 4y + 9.
Identify the like terms: 3x, −5y, 8x, 2y.
Add: (5a + 2b) and (3a − 7b).
If y = 3, find the value of 2y² + 5.
Solve: (a) x − 6 = 10 (b) 4x = 28 (c) 2x + 3 = 17.
The sum of a number and 15 is 40. Find the number.

7. Common mistakes

Mistake: Adding unlike terms. Fix: Only like terms can be added — 5x + 2y stays 5x + 2y.
Mistake: Changing only one side of an equation. Fix: Do the same operation on both sides.
Mistake: Confusing the coefficient with the variable. Fix: In 3x, the coefficient is 3, the variable is x.

8. Quick revision

Term 1 · Ch 3 · algebra.
Expression = variables + constants; term = part separated by ± ; coefficient = numerical factor.
Like terms (same variable part) can be added/subtracted; unlike cannot.
Evaluate by substitution; solve equations by the same operation on both sides.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Expression

variables + constants (e.g. 3x + 5)

Terms separated by ±.

Like terms

same variable part → add coefficients

5x + 2x = 7x.

Evaluation

substitute the value of the variable

x = 4 → 3x + 5 = 17.

Solving equations

same operation on both sides

Isolate the variable.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Adding unlike terms

✓ Only like terms can be added — 5x + 2y stays 5x + 2y.

WATCH OUT

✗ Changing only one side of an equation

✓ Do the same operation on both sides.

WATCH OUT

✗ Confusing the coefficient with the variable

✓ In 3x, the coefficient is 3, the variable is x.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Terms and coefficients

Identify terms, coefficients and like terms.

Questions

Add and subtract expressions

Combine like terms.

Questions

Solve equations and word problems

Linear equations and statement problems.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Identify

Write the coefficient of x in 7x − 4y + 9.

▶ Show solution

7.

Q2EASY· Like terms

Identify the like terms among 3x, −5y, 8x, 2y.

▶ Show solution

3x and 8x; −5y and 2y.

Q3EASY· Add

Add (5a + 2b) and (3a − 7b).

▶ Show solution

8a − 5b.

Q4MEDIUM· Evaluate

If y = 3, find the value of 2y² + 5.

▶ Show solution

2(9) + 5 = 23.

Q5MEDIUM· Solve

Solve 2x + 3 = 17.

▶ Show solution

2x = 14 → x = 7.

Q6MEDIUM· Word problem

The sum of a number and 15 is 40. Find the number.

▶ Show solution

x + 15 = 40 → x = 25.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Term 1 Chapter 3 of Samacheer Kalvi Class 7 Maths.
•Expression = variables + constants; terms are separated by + or −.
•Coefficient = the numerical factor of a term (coefficient of x in 3x is 3).
•Like terms have the same variable part and can be added/subtracted.
•Evaluate an expression by substituting the variable's value.
•Solve equations by doing the same operation on both sides.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 6-10 marks across simplification and solving

Question type	Marks each	Typical count	What it tests
Objective	1	2-4	Terms, coefficients, like terms
Simplify	2	2	Add/subtract expressions
Solve / word problem	2	2	Equations and statements

Prep strategy

Mark like terms before adding
Substitute carefully when evaluating
Keep both sides balanced when solving
Translate word problems into equations

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Problem solving

Turns real situations into equations to find unknowns.

Formulas

Science and finance use algebraic expressions.

Coding

Variables and expressions underlie programming.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Group like terms with the same colour/underline
Show substitution steps when evaluating
Write each balancing step when solving
Define the variable in word problems

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Form and solve an equation for a two-step age problem.
Simplify an expression with three different variables.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 7 Term 1 ExamHigh

NMMS / Foundation MathsMedium

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Like terms count the same kind of quantity (e.g. x's), so their coefficients can be combined; unlike terms count different quantities and cannot be merged, just as 3 apples and 2 oranges cannot be added into one number of fruit of the same kind.

An equation is a balance; to keep both sides equal, whatever you add, subtract, multiply or divide on one side you must do on the other.

Practice more, ask doubts, find a tutor

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