Page 103 - Start Up Mathematics_7

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Example 12: Subtract the sum of 3x – 5x and –x + 2x + 3 from the sum of 2 + 3x and
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7 – 2x + 2x .
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Solution: {(2 + 3x) + (7 – 2x + 2x )} – {(3x – 5x) + (–x + 2x + 3)}
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= {2x + (3x – 2x) + (2 + 7)} – {(3x – x ) + (–5x + 2x) + 3}
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= {2x + x + 9} – {2x – 3x + 3}
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= 2x + x + 9 – 2x + 3x – 3 = (2x – 2x ) + (x + 3x) + (9 – 3)
= 4x + 6
EXERCISE 6.2
1. Simplify by combining the like terms:
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(a) 3x – 4x + 11x – 2x (b) –x + 7x – 3x + 7x – 5x
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(c) 7a – 5b – ab – (2a – 3b + ab) + 3ab – b + a (d) (2x + 3y – 5) – (4 – x – x )
2. Add the following:
(a) 3ab, –4ab, 7ab, –5ab (b) x – 3xy, 7xy – y, y – x
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(c) 12x – 10y + 16xy – 8, –6x + 12y – 10xy + 16 (d) 3x y, –8xy , –6xy , –8x y
3. Simplify:
(a) (x + y – z) + (y + z – x) + (z + x – y) (b)
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(c) (x + y + 1) + (x + y – 1) + (x – y + 1) + (y + 1 – x )
4. Subtract:
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(a) –3xy from 8xy (b) 2x from –3x
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(c) (a + b – 2ab) from (a + b + 2ab) (d) (x + y ) from (2x – 3y + 4x y )
5. Subtract:
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(a) –4x y from 6x y (b) (2x – 3x + 6x + 4) from (3x – 2x + 7x + 8)
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6. Subtract the sum of (6x + 8x – 9) and (–3 + 5x – 3x ) from 10.
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7. The sum of two expressions is (x + 9x – 13). If one of them is (2x – 5x + 7), find the other.
8. Subtract (2x – 3y + 4z) from the sum of (x + 3y – 4z), (4x – y + 9z) and (–2x + 3y – z).
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9. What should be added to (3x – 2x + 3x – 1) to get (x + 2x – 6x + 5)?
–2 3 7
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10. What must be subtracted from x + xy + 2y to get 3x – 2xy – y ?
3 2 2
Value of an Expression
The value of an expression can be found by substituting the given value of literal in the expression.
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For example, value of x + 2x + 1 when x = 5 is 5 + 2 × 5 + 1 = 25 + 10 + 1 = 36.
Example 13: If m = 2, find the value of:
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(a) 2m + 1 (b) 3m – 2m + 7 (c) 9m – 5
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Solution: (a) Value of (2m + 1) when m = 2 is 2 × 2 + 1 = 4 + 1 = 5.
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(b) Value of (3m – 2m + 7) when m = 2 is 3(2) – 2(2) + 7 = 12 – 4 + 7 = 15.
9m 9(2)
(c) Value of – 5 when m = 2 is – 5 = 9 – 5 = 4.
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