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source: ncert
topic: algebra
class_level: class_8
chapter: ch2
difficulty: beginner
---
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. |