English

Linear Equations (Word Problems)

🎯 Learning Goals

  • Translate real-world problems into mathematical equations
  • Solve equations to find the correct value for the unknown 'x'

💡 Why Learn This?

Word problems help you apply math to the real world. Whether you're calculating budgets, planning a trip, or determining how many materials you need for a project, translating words to math is a critical skill.

Translating Words into Math

Word problems can look tricky, but they are just puzzles. The key is to find the unknown value, name it 'x', and express the relationships described in the text as a mathematical equation using '='.

Words ➔ Math
Total = 1000
➔ = 1000

Examples

  • Buy x apples at $2 each and a $3 basket for $11 total: 2x + 3 = 11.
  • Three times a number x plus 5 equals 26: 3x + 5 = 26.

⚠️ Common Pitfalls

The most common mistake is misinterpreting phrases like 'less than'. '5 less than a number' is written as 'x - 5', NOT '5 - x'. Always pay attention to the order of operations described in the text.

Interactive Simulator

Apples (120 yen each): 5 (5 × 120 = 600)
Oranges (80 yen each): 5 (5 × 80 = 400)
Total Cost: 1000 / Target: 1,000 yen
010

📝 Summary & Recap

  • Define the unknown quantity clearly as 'x'.
  • Look for keywords like 'is', 'totaling', or 'equals' to place your '=' sign and build the equation.

Quick Drill

Read carefully and set up the equation to solve!

3x + 5 = 14

🔍 Deep Dive (Optional)

Word problems have been used for thousands of years! Ancient Babylonian clay tablets (around 1800 BC) contain word problems about calculating the area of fields and the volume of grain, showing that math has always been deeply rooted in everyday life.

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