Page 146 - ICSE Math 7

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Example 15: 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

Example 16: When a = 0, b = –1, find the value of the given expressions:
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(a) 3a + 2b (b) a(b + b + 1) (c) (a + b)(a + 1)(b + 1)
Solution: (a) Value of 3a + 2b, when a = 0, b = –1 is 3(0) + 2(–1) = –2.
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(b) Value of a(b + b + 1), when a = 0, b = –1 is 0.
(c) Value of (a + b)(a + 1)(b + 1), when a = 0, b = –1 is (0 – 1)(0 + 1)(–1 + 1)
= (–1)(1)(0) = 0.

EXERCISE 12.4

1. If x = –1, find the value of the following expressions.
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(a) 3x – 1 (b) –3x + 2x – 1 (c) –x – x + x – 1 (d) x + x + 1
2. If x = 1 and y = –1, find the value of the following expressions.
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(a) x + y 2 (b) x + y + xy (c) 3x + 3y – 3xy (d) x + y – 2xy
3. 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
4. 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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5. 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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6. Find the value of the expression a – b + 3ab(a – b) when a = –3, b = 1.
AT A GLANCE
¾ A combination of literals (variables) and constants connected by signs of basic operations
(+, –, ×, ÷) are called algebraic expressions.
¾ In an algebraic expression, the coefficient is either a numerical factor or an algebraic factor of
product of both.

¾ The terms having exactly the same variable or algebraic factors (i.e., literals) are called like
terms. The terms not having the same variable factors are called unlike terms.

¾ The value of an expression depends on the value of the variables involved in it.

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