Page 140 - Start Up Mathematics_8 (Non CCE)

2
2
2
fi 18x – 18x + 26x = 24 – 50 (Transposing 18x and –26x to LHS and 50 to RHS)
fi 26x = –26
26x - 26
fi = (Dividing both sides by 26)
26 26
fi x = –1

EXERCISE 8.2

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
1
(d) x += ( x + 1) (e) + 15 -. 012. x = (f) (x + 4) + (x – 4) = 2x(x – 5) + 8
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
. ).05
. ).6
(x - 04 (x - 2710
(i) - (x + 61 (j) (x – 2)(x + 5) + 12 = (x + 3)(x – 4) – 2
. ) =
. 035 . 042
Ê 82 xˆ x Ê 2 - xˆ
+
(k) x - Á 3 ˜ ¯ +=3 4 - Á Ë 24 ˜ ¯
Ë
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.

px + q l
= fi m(px + q) = l(rx + t)
rx t+ m
Now find the solution by transposition.

2x - 1 4
Example 8: 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
fi = (Dividing both sides by 14)
14 14

9
fi x = is the required solution.
14

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