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⚖️ Writing Simple Equations

Turn 'I think of a number...' puzzles into equations like 2n + 5 = 17, and hunt down all the pairs of numbers that make statements like a + b = 12 true.

3
lessons
~20 min
to learn
🔢 Math
subject
Ages 6–12
level
Start the course →

What you’ll learn

  1. Letters for UnknownsUse letters for unknowns and translate word problems into algebraic equations.A letter stands for a mystery number, so 'double it and add 5 to get 17' becomes 2n + 5 = 17. Each phrase has a symbol translation: 'double' is 2n, 'three times, less 1' is 3n - 1. Writing the equation is the first step to solving the puzzle.
  2. Solving One-Step EquationsSolve one-step equations by using inverse operations and keeping both sides balanced.Solving means undoing operations with their opposites while keeping the scale balanced: for 3x = 24, divide both sides by 3 to get x = 8. For 2n + 5 = 17, subtract 5 then divide by 2 to get n = 6. Always check by putting the answer back in.
  3. Pairs That FitFind all number pairs that satisfy an equation with two unknowns, working systematically.With two letters, many pairs can fit. For a + b = 12 (both above zero), let a run 1 to 11 and b follows - 11 pairs, none missed. For 2x + y = 20, choose x and solve for y, as with (5, 10). Working in order guarantees you catch every solution.

Questions this course answers

How do you write 'I think of a number, double it, and add 5 to get 17'?

Double the number is 2n, plus 5 equals 17.

What does the letter in an equation stand for?

A letter is a placeholder for an unknown number.

To solve 3x = 24, what do you do to both sides?

Undo the multiply by dividing both sides by 3.

Why does a + b = 12 have many answers but 3x = 24 has just one?

Two unknowns allow many combinations; one unknown pins down a single value.

Grounded in trusted sources

  • Khan Academy
  • BBC Bitesize - Maths
  • NRICH - University of Cambridge
  • Math is Fun

Every Wunder lesson is built from real, reputable sources — never invented.

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