Page 141 - Start Up Mathematics_8 (Non CCE)

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Example 9: Solve + = .
x + 2 x + 3 x + 9
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Solution: + =
x + 2 x + 3 x + 9
x ++ +3 x 2 2
fi = (Taking LCM of LHS)
( x + 2)( x + 3) x + 9
fi (2x + 5)(x + 9) = 2(x + 2)(x + 3) (Cross-multiply)

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fi 2x + 18x + 5x + 45 = 2x + 10x + 12
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fi 2x – 2x + 23x – 10x = 12 – 45 (Transposing 2x , 10x to LHS and 45 to RHS)
fi 13x = –33
13x - 33
fi = (Dividing both sides by 13)
13 13
-33
fi x = is the required solution.
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3x + 8 Ê 12x - ˆ x 7x Ê 2x + 16ˆ
Example 10: Solve: - Á ˜ + = - Á ˜
16 Ë 15x - 30¯ 3 12 Ë 32 ¯
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3x + 8 Ê 12x - ˆ x 7x Ê 2x + 16ˆ
Solution: - Á ˜ + = - Á ˜
16 Ë 15x - 30¯ 3 12 Ë 32 ¯
3x + 8 x 7x 2x + 16 12x - 6
fi + - + =
16 3 12 32 15x - 30

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7x Ê 2x + 16ˆ Ê 12x - ˆ
(Transposing and - Á ˜ to LHS and - Á ˜ to RHS)
12 Ë 32 ¯ Ë15x - 30 ¯
LCM of 16, 3, 12, 32 = 96. On multiplying both sides by 96, we get
Ê 3x + 8ˆ Ê xˆ Ê 7xˆ Ê 2x + 16ˆ Ê 12x -- ˆ
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fi 96 Á 16 ¯ ˜ + 96 Á ˜ - 96 Á Ë 12 ¯ + 96 Á Ë 32 ˜ = 96 Á Ë15x - 30 ˜ ¯
˜
3¯
Ë
¯
Ë
Ê 12x - ˆ
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fi 6(3x + 8) + 32x – 8(7x) + 3(2x + 16) = 96 Á 15x - 30¯ ˜
Ë
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Ê 12x - ˆ
fi 18x + 48 + 32x – 56x + 6x + 48 = 96 Á 15x - 30¯ ˜
Ë
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Ê 12x - ˆ
fi 96 = 96 Á Ë 15x - 30¯
˜
96 96 12 -( x 6)
fi = (Dividing both sides by 96)
96 96 15 -x 30)
(
12 -x 6 12x - 6 1
fi 1 = fi = (Cross-multiply)
15 -x 30 15x - 30 1
fi 12x – 6 = 15x – 30
fi 12x – 15x = –30 + 6 (Transposing 15x to LHS and –6 to RHS)
fi –3x = – 24 fi 3x = 24

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