Page 105 - Start Up Mathematics_7

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Example 20: Find the value of a that will make the expression 3x – 8x + a equal to 5, when x = 2.
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Solution: Value of 3x – 8x + a, when x = 2 is 3(2) – 8(2) + a = 12 – 16 + a = a – 4
Now, a – 4 = 5 ⇒ a = 9
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Example 21: Find the value of m if the expression x – 5x + mx – 4 equals –1 when x = –1.
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Solution: The value of (x – 5x + mx – 4) is –1, when x = –1
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∴ (–1) – 5(–1) + m(–1) – 4 = –1
⇒ 1 + 5 – m – 4 = –1
⇒ 2 – m = –1
⇒ –m = –1 – 2 = –3

⇒ m = 3

EXERCISE 6.3

1. If x = 3, find the value of the following:

(a) x + 3 (b) 3x – 6 (c) 9 – 3x (d)
2. If x = –1, find the value of the following:

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(a) 3x – 1 (b) –3x + 2x – 1 (c) –x – x + x – 1 (d) x + x + 1
3. If x = 1 and y = –1, find the value of the following:
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(a) x + y 2 (b) x + y + xy (c) 3x + 3y – 3xy (d) x + y – 2xy
4. Find the value of the following expressions when x = 0, y = –2.
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(a) x + y + 2xy (b) x – y (c) 2x + 2y – xy (d) x – xy + y 2
5. Simplify the expressions and find the value when x = –2.
(a) 3(x + 5) – x – 7 (b) x + 5 – 2(x – 5) (c) 2(4x – 1) + 4(2x + 1)
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6. What should be the value of p if the value of 3x + 4x – p is 5, when (a) x = –1, (b) x = 1?
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7. Find the value of the expression a – b + 3ab(a – b) when a = –3, b = 1.
Use of Algebraic Expressions
Algebraic expressions are used to write certain rules or formulas in a concise but general form.
For example, area of a rectangle = l × b, where l = length of the rectangle and b = breadth of the
rectangle
The number of diagonals that can be drawn from a vertex of a quadrilateral, pentagon, hexagon,
..., etc. are 1, 2, 3, ... . Generalising this, we can say that the number of diagonals which can be
drawn from any one vertex of a polygon having n sides is (n – 3).

D E D F E
C

A D
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A B
B B C

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