Page 64 - SM inner class 8.cdr

-
160 63 97 116 6 9
= = = - ´
200 200 100 10 8
Verification: 116 27
= -
R.H.S. = 1.16 - 0.6x 100 40
232 135 97
-
Putting x = 9/8, we get: = =
9 200 200
= 1.16 - 0.6 ´
8 Since, L.H.S. = R.H.S. hence verified.

E xercise 8.1

1. Solve each of the follow ing equa tions.
1
(i) 7x + 2 = -19 (ii) 3x - = 5 (iii) 5x - 4 = 21
3
(iv) -7x = 21 (v) 18 - 7x = -3 (vi) 3(x + 4) = 21
2x 3x
(vii) - = 8 (viii) 3x - 9 = 5x - 3 (ix) 3(x - 3) = 4(2x + 1)
3 5
2. Solve each of the follow ing equa tions and check your solu tion by substi tut ing in the equa tion.
3x 1 x x
(i) - 10 = (ii) - = 8
2 2 2 3
(iii) 6x - 9 - 2(1 - x) = x + 9 (iv) 2(x - 2) - 5(x - 5) = 4(x - 8) - 2(x - 2)
2 - y 3 (3x + ) 2 - 3
(v) = (vi) =
y + 7 5 (2x - ) 3 2
(x -8 ) (x -3 )
(vii) = (viii) 0.25(4y - 3) = 0.5y - 9
3 5
z 4
(ix) 3(5 - x) - 2(5 + x) = 3(x + 1) (x) =
z +15 9
2x + 4
(xi) = x + 2
2
Word problems on linear equations Example 7. The denominator of a rational
number is greater than its numerator by 3. If
We have learnt how to form linear equations in
the numerator is increased by 7 and the
one variable. We will now study some
denominator is decreased by 1, the new
applications of linear equations. 3
number becomes . Find the original number.
Example 6: The three angles in a triangle are 2
in the ratio of 2:3:4. Find the measure of each Solution: Let the numerator of a rational
angle.
number = x.
Solution : Let the ratio = x
Then the denominator of a rational number
As in the triangle, sum of all the three angles = = x + 3.
180°
When numerator is increased by 7, then new
\ 2x + 3x + 4x = 180 numerator = x + 7
9x = 180 When denominator is decreased by 1, then new
x = 20 denominator = x + 3 - 1

Each angle, 2x = 2(20) = 40° 3
The new number formed =
3x = 3(20) = 60° 2
4x = 4(20) = 80°

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Mathematics In Focus - 8