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Grade 8/ Mathematics/ Algebra Play
Chapter 13 · NCERT Class 8 Ganita Prakash

Algebra Play

Let a letter stand in for a number you don't yet know, write what you do know as an equation, then keep it balanced until the letter gives up its secret. From "x" to "x = 7" — tap each idea to play along.

📐 3 topics⏱ ~25 min📝 12-question quiz
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The building blocks of algebra

Variables build into terms, terms into expressions, expressions into equations you can solve. Tap each block to see how it fits the next.

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The three big ideas

  • A variable is a letter (x, y, n) standing for an unknown or changing value.
  • A term is a single piece like 7x or 5. In 7x, the 7 is the coefficient and x is the variable; a lone number like 5 is a constant.
  • An expression joins terms with + or −, e.g. 3x + 5. It has no equals sign.
  • Like terms have the same variable to the same power and can be combined: 5x + 2x = 7x, but 5x + 2 cannot be merged.
Common mistake: combining unlike terms — writing 5x + 3 = 8x. The 3 is a constant, not an "x", so it stays separate: 5x + 3.
  • A linear equation in one variable sets two expressions equal, with the variable to the first power: 3x + 5 = 20.
  • The balance rule — do the same operation to both sides and the equation stays true.
  • Transposing is a shortcut: move a term across the = and flip its sign (+ becomes −, × becomes ÷).
  • Variables on both sides — gather the variable terms on one side and the numbers on the other, then solve.

Worked example. Solve 3x + 5 = 20.

1. Subtract 5 from both sides: 3x + 5 − 5 = 20 − 5 → 3x = 15.

2. Divide both sides by 3: 3x ÷ 3 = 15 ÷ 3 → x = 5.

3. Check: put x = 5 back in: 3(5) + 5 = 15 + 5 = 20. ✓

Common mistake: changing only one side. If you subtract 5 from the left, you must subtract 5 from the right too — otherwise the balance breaks.
  • Step 1 — name the unknown. Let x stand for what the question asks.
  • Step 2 — translate. "More than" → +, "less than" → −, "times" → ×, "is" → =.
  • Step 3 — solve the equation with the balance method.
  • Step 4 — check the answer makes sense in the original words.

Worked example. Reena is 4 years older than twice her brother's age. Reena is 18. How old is her brother?

1. Let the brother's age be x.

2. "Twice his age plus 4" = 2x + 4, and this equals Reena's age 18 → 2x + 4 = 18.

3. Subtract 4 from both sides: 2x = 14. Divide by 2: x = 7.

4. Check: twice 7 is 14, plus 4 is 18 = Reena's age. ✓ The brother is 7 years old.

Where you'll meet it

Algebra solving real puzzles

Splitting a bill

Four friends share a meal that costs ₹520 plus a ₹40 delivery fee. If each pays the same amount x, then 4x + 40 = 520, so x = ₹120 each. One equation settles the share fairly.

Filling a water tank

A tank already holds 50 litres and a pump adds 15 litres each minute. To reach 200 litres: 50 + 15t = 200, giving t = 10 minutes. Algebra predicts the wait before you ever turn on the pump.

Guess-my-number games

"I think of a number, double it, add 3, and get 17." That is 2x + 3 = 17, so x = 7. Every number-trick puzzle is really a hidden linear equation.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.

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Interactive built to the OpenMAIC approach (THU-MAIC, MIT). Content from the NCERT Class 8 Ganita Prakash textbook (ncert.nic.in).

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