Page 126 - Maths Skills - 7

124 Maths

Example 5: What should be added to 3x – xy + 7y to obtain 2x – 3xy + y ?
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Solution: Translating into an equation, we get
(3x – xy + 7y ) + A = 2x – 3xy + y 2
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⇒ Required solution (A) = (2x – 3xy + y ) – (3x – xy + 7y )
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= 2x – 3xy + y – 3 + xy – 7y = 2x – 3x – 3xy + xy + y – 7y = – x – 2xy – 6y 2
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Hence, –x – 2xy – 6y must be added.
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Example 6: What should be subtracted from 20x + 7x + 1 to get 2x – 7x + 10?
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Solution: Translating the statement into equation, we get
20x + 7x + 1 – A = 2x – 7x + 10
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⇒ A = 20x + 7x + 1 – (2x – 7x + 10) = 20x + 7x + 1 –2x + 7x – 10
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= 20x – 2x + 7x + 7x + 1 – 10 = 18x + 14x – 9
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Example 7: By how much does x – 8x + 7 exceed 3x – 5 + 9x?
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Solution: Translating the statement into equation, we get
A = (x – 8x + 7) – (3 – 5 + 9x) = x – 8x + 7 – 3x + 5 – 9x
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= x – 3x – 8x – 9x + 7 + 5 = –2x – 17x + 12
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Example 8: By how much is x + 3x + y smaller than 3x – y + 11x?
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Solution: Required solution = (3x – y + 11x) – (x + 3x + y) = 3x – y + 11x – x – 3x – y
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= 3x – x – y – y + 11x – 3x = 2x – 2y + 8x
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Exercise 7.2
1. Add the following:
(i) a – 2c + b, – a + b, 6a – 4c + b (ii) 3x + 7x + 7, 9x – 2x + 5
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(iii) 2x + 15x + 7x – 1, 4x – x + 9x + 2x + 11 (iv) 62t – 32t + 45, 24t + 19t – 12
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(v) p + pq + p q + q , 2p + pq – 3p + q , 3p + 2pq + 2p q + 3q 2
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2. Subtract the following:
 1   1 1
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(i)  4x − x + 7 −− 2x − x +  (ii) p – q from 3p – 5q + 7pq
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 5   2 3
(iii) g + h – 2gh from g + h + 2gh (iv) 35x + 30x – 14 from x + 10x + 28
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(v) 10x – 4x + 11 from 9x + 3x – 2x + 4
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3. Subtract 9a – 7b + 5c from the sum of (a – 2b + 3c),  1 a + 2b − 6c and 19b – 3c + a.
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4. Subtract the sum of (– x + 13x + 6x ) and (6x + 5x + 7x ) from 19x + 7x – 2x .
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5. Take away 10x + 7x + 5x from –7x + 14 – 2x.
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