Page 167 - ICSE Math 8

Ê 2 - xˆ Ê 2 - ˆ x
fi 12x – 3 x - 6 ˜ ¯ = 4(2x + 8) – 36 fi 12x – 3x + 3 Á Ë 6 ¯ ˜ = 8x + 32 – 36
Á
Ë
-
2 − x Ê 2 xˆ
fi 9x + = 8x – 4 fi 2 9x + ˜ = 2(8x – 4) (Multiplying both sides by 2)
Á
2 Ë 2 ¯
fi 18x + 2 – x = 16x – 8
fi 17x + 2 = 16x – 8 fi 17x – 16x = –8 – 2 (Transposing 16x to LHS and 2 to RHS)
fi x = –10
Example 6: Solve 0.25(4f – 3) = 0.05(10f – 9) and check the solution.

Solution: 0.25(4f – 3) = 0.05(10f – 9) fi 0.25 × 4f – 0.25 × 3 = 0.05 × 10f – 0.05 × 9
fi 1.0f – 0.75 = 0.5f – 0.45 fi f – 0.75 = 0.5f – 0.45
fi f – 0.5f = –0.45 + 0.75 (Transposing 0.5f to LHS and –0.75 to RHS)
05. f 030. 03.
fi 0.5f = 0.30 fi 05. = 05. = 05. (Dividing both sides by 0.5)

3
fi f = = 0.6
5

EXERCISE 15.2

Solve the following equations using transposition method and check the solution.
x - 4 x - 3 1 3x - 2 2 2x + 3
(a) - = (b) += - (c) 15(x – 4) – 2(x – 9) + 5(x + 6) = 0
x
2 4 6 4 3 3
2 3 x (. x)
05 +
2
2
(d) x += ( x + 1) (e) + 15 -. 012. x = (f) (x + 4) + (x – 4) = 2x(x – 5) + 8
1
3 4 3 2
5x - 2 1 Ê 2 x- ˆ 12
2
2
2
(g) - Á 3x - ˜ = (h) {(3x + 5) + (x + 2)} + {(3x + 5) – (x + 2)} = 20x – 78
4 5 Ë 6 ¯ 5
+
Ê 82 xˆ x Ê 2 - xˆ
(i) (x – 2)(x + 5) + 12 = (x + 3)(x – 4) – 2 (j) x - Á Ë 3 ˜ ¯ +=3 4 - Á ˜
¯
Ë 24
Solving Equations Reducible to the Linear Form (Cross-Multiplication Method)
px + q l
Let there be an equation in the form = .
rx t+ m
First convert the equation to linear form by the method of cross-multiplication and then find the solution by
transposition.
px + q l
= fi m(px + q) = l(rx + t)
rx t+ m
2x - 1 4
Example 7: Solve: =
5x - 3 3
2x - 1 4
Solution: = (Cross-multiply)
5x - 3 3
fi 3(2x –1) = 4(5x – 3) fi 6x – 3 = 20x – 12
fi 6x – 20x = –12 + 3 (Transposing 20x to LHS and –3 to RHS)
fi –14x = –9 fi 14x = 9
14x 9 9
fi = fi x = is the required solution. (Dividing both sides by 14)
14 14 14

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