x 3 x + 3 = 8 Come play with numbers!
Variables & constants

What stays still while something else changes?

# Variable vs constant - A **variable** can change: `x`, `n`, `t` - A **constant** stays fixed: `7`, `−3`, `π` (about 3.14) In `3x + 5`: - `x` is the variable - `3` is a coefficient (how many x) - `5` is a constant term ## Real life - Variable: number of samosas you buy - Constant: price of one samosa today (say ₹12) - Total: `12n` Tomorrow the price might change — then 12 is no longer that constant. In **one** problem, treat given numbers as fixed. ## Variable vs constant — a kitchen test Open a recipe. - Number of guests can change → variable - “1 teaspoon of salt per litre” may be treated as constant in that recipe In `3x + 5`: | Piece | Name | Role | | --- | --- | --- | | x | variable | the changing / unknown number | | 3 | coefficient | how many x | | 5 | constant term | a fixed add-on | ### Coefficient of a bare letter `x` means `1x`. Coefficient is **1**, not “nothing”. `−y` means `−1y`. Coefficient is **−1**. Write the invisible 1 until it becomes automatic.

By the end of this lesson

Point at the variable, the coefficient, and the constant term in an expression such as 3x + 5.

Remember

  • Variable = can change (x, n, t).
  • Constant = stays fixed in this problem (7, −3, 12).
  • Coefficient = the number glued to the variable (in 3x the 3).
  • In 12n, 12 is the price (constant here) and n is how many (variable).
  • A number that is fixed today might change in a new problem tomorrow.

Worked examples

Cover the answer. Try the steps on paper, then open them.

Example 1 — Label 7n − 4

Name the variable, coefficient, and constant term.

  1. Variable: n
  2. Coefficient of n: 7
  3. Constant term: −4 (keep the sign)

Answer: n ; 7 ; −4

Check: The sign belongs to the constant.

Example 2 — Samosa stall

One samosa is ₹15. You buy n of them. Write total and name each part.

  1. Total = 15n
  2. 15 is constant in this stall today
  3. n is variable — you might buy 2 or 6

Answer: 15n

Check: If n = 4, total = 60.

Example 3 — 3x + 5 with two values of x

Evaluate when x = 2 and when x = 10.

  1. x = 2 → 3(2) + 5 = 11
  2. x = 10 → 3(10) + 5 = 35
  3. 3 and 5 stayed still; x moved.

Answer: 11 and 35

Check: That is why x is called a variable.

Common mistakes

Slip Calling 3 the variable in 3x + 5.

Fix 3 is a coefficient. x is the variable.

The letter is what can stand for different numbers.

Slip Dropping the minus on a constant: calling −4 just 4.

Fix The constant term is −4.

Signs travel with the term.

Slip Saying “constants never change in life”.

Fix They are fixed inside one problem.

Tomorrow the samosa price can change — new problem, new constant.

Try on paper first

Write the answer, then tap Reveal. These are not the quiz — they are warm-ups.

1. In 9y + 2, what is the constant term?

Answer: 2

2. In 9y + 2, what is the coefficient of y?

Answer: 9

3. In −x + 6, what is the coefficient of x?

Answer: −1

−x means −1 × x.

4. Name a variable you would pick for “number of minutes”.

Answer: t or m (any letter is fine if you define it)

Touch practice

8 tap / type

Tap an option or type the answer. Retry any miss. Extra generated questions appear after the set if this topic allows it.

Optional picture lab

After practice

Real world

Today’s snack price is fixed; how many you buy changes.

Connect

Constants in code stay put; variables update.

⭐ Star quiz

9 questions

Finish the touch practice first if you can. Then answer without peeking. Read every “why”.

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