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Exercise - 2.6

Linear Equations in One Variable

**Question-1 :-** Solve (8x - 3)/3x = 2 .

(8x - 3)/3x = 2 8x - 3 = 2 x 3x 8x = 3 + 6x 8x - 6x = 3 2x = 3 x = 3/2 Verification : L.H.S = (8x - 3)/3x = (8 x 3/2 - 3)/(3 x 3/2) = (12 - 3)/(9/2) = (9 x 2)/9 = 2 = R.H.S

**Question-2 :-** Solve 9x/(7 - 6x) = 15 .

9x/(7 - 6x) = 15 9x = 15 x (7 - 6x) 9x = 105 - 90x 9x + 90x = 105 99x = 105 x = 105/99 x = 35/33 Verification : L.H.S = 9x/(7 - 6x) = [(9 x 35)/33] ÷ [7 - (6 x 35/33)] = (3 x 35/11) ÷ [7 - (2 x 35/11)] = (105/11) ÷ (7 - 70/11) = (105/11) ÷ [(77 - 70)/11] = 105/11 ÷ 7/11 = 105/7 = 15 = R.H.S

**Question-3 :-** Solve z/(z + 15) = 4/9 .

z/(z + 15) = 4/9 9z = 4 x (z + 15) 9z = 4z + 60 9z - 4z = 60 5z = 60 z = 60/5 z = 12 Verification : L.H.S = z/(z + 15) = 12/(12 + 15) = 12/27 = 4/9 = R.H.S

**Question-4 :-** Solve (3y + 4)/(2 - 6y) = -2/5 .

(3y + 4)/(2 - 6y) = -2/5 5 x (3y + 4) = -2 x (2 - 6y) 15y + 20 = -4 + 12y 15y - 12y = -4 - 20 3y = -24 y = -24/3 y = -8 Verification : L.H.S = (3y + 4)/(2 - 6y) = (-24 + 4)/(2 + 48) = -20/50 = -2/5 = R.H.S

**Question-5 :-** Solve (7y + 4)/(y + 2) = -4/3 .

(7y + 4)/(y + 2) = -4/3 3 x (7y + 4) = -4 x (y + 2) 21y + 12 = -4y - 8 21y + 4y = -8 - 12 25y = -20 y = -20/25 y = -4/5 Verification : L.H.S = (7y + 4)/(y + 2) = (-28/5 + 4) ÷ (-4/5 + 2) = [(-28 + 20)/5] ÷ [(-4 + 10)/5] = (-8/5) ÷ (6/5) = (-8 x 5)/(5 x 6) = -8/6 = -4/3 = R.H.S

**Question-6 :-** The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.

Let the age of Hari = 5x years the age of Harry = 7x years According to question : (5x + 4)/(7x + 4) = 3/4 4 (5x + 4) = 3 (7x + 4) 20x + 16 = 21x + 12 20x - 21x = 12 - 16 -x = -4 x = 4 The age of Hari = 5x = 5 x 4 = 20 years The age of Harry = 7x = 7 x 4 = 28 years

**Question-7 :-** The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number
obtained is 3/2. Find the rational number.

Let the numerator of a rational number = x the denominator = x + 8 rational number = x/(x+8) According to question : (x + 17)/(x + 8 - 1) = 3/2 (x + 17)/(x + 7) = 3/2 2 (x + 17) = 3 (x + 7) 2x + 34 = 3x + 21 2x - 3x = 21 - 34 -x = -13 x = 13 The numerator of a rational number = x = 13 The denominator = x + 8 = 13 + 8 = 23 Rational number = x/(x + 8) = 13/(13 + 8) = 13/21

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