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CLASS VII • ALGEBRA Chapter 7: Finding the Unknown

Finding the Unknown

Move from balance-scale thinking to equations, matchstick patterns, systematic solving, checking solutions, and real-life word problems.

Fact Sheet: Finding Unknown Values

An equation is a statement that two expressions are equal. Solving an equation means finding the value of the unknown that makes the left hand side equal to the right hand side.

Balance idea: If equal weights are removed from both pans of a balanced scale, it remains balanced.
Equation idea: If the same operation is done on both sides, equality is preserved.
Matchstick pattern: If the nth arrangement has 2n + 1 sticks, then 99 sticks gives 2n + 1 = 99, so n = 49.
x4
=
12

x + 4 = 12remove 4 from both sidesx = 8

Equation Hub

Equation

A statement of equality between two expressions.

Example: 2n + 1 = 99.

LHS and RHS

LHS is the left hand side. RHS is the right hand side.

Solution makes LHS = RHS.

Balance Rule

Do the same operation to both sides.

Equality stays true.

Add/Subtract Inverses

To remove +7, subtract 7.

2y + 7 = 21 → 2y = 14.

Multiply/Divide Inverses

To remove factor 5, divide by 5.

5x = 11 → x = 11/5.

Check Solution

Substitute your answer into the original equation.

Both sides must match.

Online Lab: Equation Solver

Score: 0Current Streak: 🔥 0Badge: Unknown Finder


Activity Zone

⚖️ Balance Scale Solver

Solve equations of the form ax + b = c.

=

🔥 Matchstick Pattern Lab

The nth arrangement uses 2n + 1 matchsticks.

🧱 Tile Pattern: 3k + 1

Use the tile pattern rule from the chapter. Step k has 3k + 1 tiles.

🧮 Equation Stepper

Solve selected equations step-by-step.

🎩 Math Trick Reverse Machine

Think of a number, subtract 3, multiply by 4, then add 8. Reverse the trick from the final answer.

📋 Check LHS = RHS

Substitute the proposed solution and check if it works.

Worksheet Generator

Generate practice on balance equations, matchstick patterns, systematic solving, checking solutions, and word problems.



Real-World Use

Party Budget: If each plate costs ₹25 and delivery is ₹50, then total cost is 25p + 50.
Savings: If two people save different starting amounts and monthly amounts, equations find when their savings become equal.
Patterns: If step k has 3k + 1 tiles, equations can tell whether a target number of tiles is possible.

🌍 Real-Life Case Generator

Teacher Tools

Learning Outcomes

  • Represent unknown quantities using letter-numbers.
  • Frame equations from balance scales and patterns.
  • Solve one-step and two-step equations systematically.
  • Use inverse operations while preserving equality.
  • Check solutions by substituting into the original equation.
  • Apply equations to matchstick, tile, budget, savings, and math-trick problems.

Exit Ticket Prompts

  • Solve 2n + 1 = 99 and explain each step.
  • Frame an equation for a 4-column matchstick or tile pattern.
  • Check whether x = 11/5 satisfies 5x - 4 = 7.
  • Create an equation that has no solution.