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| source: ncert |
| topic: algebra |
| class_level: class_8 |
| chapter: ch2 |
| difficulty: beginner |
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| Class 8 | Ch2: Linear Equations in One Variable |
| Linear equation: variable has power 1 only. ax+b=c form. |
| Can involve fractions and variables on both sides. |
| SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES: |
| Collect variable terms on one side, constants on other. |
| 3x+2=5x-4 → 2+4=5x-3x → 6=2x → x=3. |
| SOLVING EQUATIONS WITH FRACTIONS: |
| Multiply both sides by LCM of all denominators to clear fractions. |
| (2x+3)/5-(x-4)/3=2. LCM=15. Multiply: 3(2x+3)-5(x-4)=30. |
| 6x+9-5x+20=30 → x+29=30 → x=1. |
| WORD PROBLEMS - STANDARD TYPES: |
| Age problems: Let present age=x. Set up equation from given conditions. |
| Number problems: Let number=x. Translate words to equation. |
| Geometry problems: Use perimeter/area formulas. |
| Money/mixture problems: Set up equation for totals. |
| SOLVED EXAMPLES: |
| Example 1: (2x+3)/5-(x-4)/3=2 |
| Multiply by 15: 3(2x+3)-5(x-4)=30 → 6x+9-5x+20=30 → x=1. |
| Verify: (2+3)/5-(1-4)/3=1+1=2. Correct. |
| Example 2: A number is 4 more than twice another. Sum=40. |
| Let numbers be x and 2x+4. x+(2x+4)=40 → 3x=36 → x=12. |
| Numbers: 12 and 28. Verify: 12+28=40 and 28=2(12)+4. Correct. |
| Example 3: Present age ratio of A and B is 3:4. After 5 years ratio becomes 4:5. Find ages. |
| Let ages: 3x and 4x. (3x+5)/(4x+5)=4/5 → 15x+25=16x+20 → x=5. |
| Ages: 15 and 20. |
| COMMON MISTAKES: |
| When multiplying by LCM, multiply EVERY term including constants. |
| Verify answer by substituting back in ORIGINAL equation. |
