### Chapter 9 Linear Equation In One Variable – Exercise 9.2 | Set 1

**Question 14. (1-2x)/7 â€“ (2-3x)/8 = 3/2 + x/4**

**Solution:**

(1-2x)/7 â€“ (2-3x)/8 = 3/2 + x/4

First rearrange the equation

(1-2x)/7 â€“ (2-3x)/8 â€“ x/4 = 3/2

By taking LCM for 7, 8 and 4 which is 56

((1-2x)8 â€“ (2-3x)7 â€“ 14x)/56 = 3/2

(8 â€“ 16x â€“ 14 + 21x â€“ 14x)/56 = 3/2

(-9x â€“ 6)/56 = 3/2

After cross-multiplying

2(-9x-6) = 3(56)

-18x â€“ 12 = 168

-18x = 168+12

-18x = 180

x = 180/-18

x = -10

Now verify the equation by putting x = -10

(1-2x)/7 â€“ (2-3x)/8 = 3/2 + x/4

x = -10

(1-2(-10))/7 â€“ (2-3(-10))/8 = 3/2 + (-10)/4

(1+20)/7 â€“ (2+30)/8 = 3/2 â€“ 5/2

21/7 â€“ 32/8 = 3/2 â€“ 5/2

3 â€“ 4 = -2/2

-1 = -1

Thus, L.H.S. = R.H.S.,

Hence, the equation is verified.

**Question 15. (9x+7)/2 â€“ (x â€“ (x-2)/7) = 36**

**Solution:**

(9x+7)/2 â€“ (x â€“ (x-2)/7) = 36

First simplify the given equation

(9x+7)/2 â€“ (7x-x+2)/7 = 36

(9x+7)/2 â€“ (6x+2)/7 = 36

By taking LCM for 2 and 7 is 14

(7(9x+7) â€“ 2(6x+2))/14 = 36

(63x+49 â€“ 12x â€“ 4)/14 = 36

(51x + 45)/14 = 36

After cross-multiplying

51x + 45 = 36(14)

51x + 45 = 504

51x = 504-45

51x = 459

x = 459/51

x = 9

Now verify the equation by putting x = 9

(9x+7)/2 â€“ (x â€“ (x-2)/7) = 36

(9x+7)/2 â€“ (6x+2)/7 = 36

x = 9

(9(9)+7)/2 â€“ (6(9)+2)/7 = 36

(81+7)/2 â€“ (54+2)/7 = 36

88/2 â€“ 56/7 = 36

44 â€“ 8 = 36

36 = 36

Thus, L.H.S. = R.H.S.,

Hence, the equation is verified.

**Question 16. 0.18(5x â€“ 4) = 0.5x + 0.8**

**Solution:**

0.18(5x â€“ 4) = 0.5x + 0.8

First rearrange the given equation

0.18(5x â€“ 4) â€“ 0.5x = 0.8

0.90x â€“ 0.72 â€“ 0.5x = 0.8

0.90x â€“ 0.5x = 0.8 + 0.72

0.40x = 1.52

x = 1.52/0.40

x = 3.8

Now verify the equation by putting x = 3.8

0.18(5x â€“ 4) = 0.5x + 0.8

x = 3.8

0.18(5(3.8)-4) = 0.5(3.8) + 0.8

0.18(19-4) = 1.9 + 0.8

2.7 = 2.7

Thus L.H.S. = R.H.S.,

Hence, the equation is verified

**Question 17. 2/3x â€“ 3/2x = 1/12**

**Solution:**

2/3x â€“ 3/2x = 1/12

By taking LCM for 3x and 2x which is 6x

((2Ã—2) â€“ (3Ã—3))/6x = 1/12

(4-9)/6x = 1/12

-5/6x = 1/12

After cross-multiplying

6x = -60

x = -60/6

x = -10

Now verify the equation by putting x = -10

2/3x â€“ 3/2x = 1/12

x = -10

2/3(-10) â€“ 3/2(-10) = 1/12

-2/30 + 3/20 = 1/12

((-2Ã—2) + (3Ã—3))/60 = 1/12

(-4+9)/60 = 1/12

5/60 = 1/12

1/12 = 1/12

Thus L.H.S. = R.H.S.,

Hence the equation is verified.

**Question 18. 4x/9 + 1/3 + 13x/108 = (8x+19)/18**

**Solution:**

4x/9 + 1/3 + 13x/108 = (8x+19)/18

First rearrange the given equation

4x/9 + 13x/108 â€“ (8x+19)/18 = -1/3

By taking LCM for 9, 108 and 18 which is 108

((4xÃ—12) + 13xÃ—1 â€“ (8x+19)6)/108 = -1/3

(48x + 13x â€“ 48x â€“ 114)/108 = -1/3

(13x â€“ 114)/108 = -1/3

After cross-multiplying

(13x â€“ 114)3 = -108

39x â€“ 342 = -108

39x = -108 + 342

39x = 234

x = 234/39

x = 6

Now verify the equation by putting x = 6

4x/9 + 1/3 + 13x/108 = (8x+19)/18

x = 6

4(6)/9 + 1/3 + 13(6)/108 = (8(6)+19)/18

24/9 + 1/3 + 78/108 = 67/18

8/3 + 1/3 + 13/18 = 67/18

((8Ã—6) + (1Ã—6) + (13Ã—1))/18 = 67/18

(48 + 6 + 13)/18 = 67/18

67/18 = 67/18

Thus, L.H.S. = R.H.S.,

Hence, the equation is verified.

**Question 19. (45-2x)/15 â€“ (4x+10)/5 = (15-14x)/9**

**Solution:**

(45-2x)/15 â€“ (4x+10)/5 = (15-14x)/9

First rearranging the given equation

(45-2x)/15 â€“ (4x+10)/5 â€“ (15-14x)/9 = 0

By taking LCM for 15, 5 and 9 which is 45

((45-2x)3 â€“ (4x+10)9 â€“ (15-14x)5)/45 = 0

(135 â€“ 6x â€“ 36x â€“ 90 â€“ 75 + 70x)/45 = 0

(28x â€“ 30)/45 = 0

After cross-multiplying

28x â€“ 30 = 0

28x = 30

x = 30/28

x = 15/14

Now verify the equation by putting x = 15/14

(45-2x)/15 â€“ (4x+10)/5 = (15-14x)/9

x = 15/14

(45-2(15/14))/15 â€“ (4(15/14) + 10)/5 = (15 â€“ 14(15/14))/9

(45- 15/7)/15 â€“ (30/7 + 10)/5 = (15-15)/9

300/105 â€“ 100/35 = 0

(300-300)/105 = 0

0 = 0

Thus, L.H.S. = R.H.S.,

Hence, the equation is verified.

**Question 20. 5(7x + 5)/3 â€“ 23/3 = 13 â€“ (4x-2)/3**

**Solution:**

5(7x+5)/3 â€“ 23/3 = 13 â€“ (4x-2)/3

First rearrange the given equation

(35x + 25)/3 + (4x â€“ 2)/3 = 13 + 23/3

(35x + 25 + 4x â€“ 2)/3 = (39+23)/3

(39x + 23)/3 = 62/3

After cross-multiplying

(39x + 23)3 = 62(3)

39x + 23 = 62

39x = 62 â€“ 23

39x = 39

x = 1

Now verify the equation by putting x = 1

5(7x+5)/3 â€“ 23/3 = 13 â€“ (4x-2)/3

x = 1

(35x + 25)/3 â€“ 23/3 = 13 â€“ (4x-2)/3

(35+25)/3 â€“ 23/3 = 13 â€“ (4-2)/3

60/3 â€“ 23/3 = 13 â€“ 2/3

(60-23)/3 = (39-2)/3

37/3 = 37/3

Thus, L.H.S. = R.H.S.,

Hence, the equation is verified.

**Question 21. (7x-1)/4 â€“ 1/3(2x â€“ (1-x)/2) = 10/3**

**Solution:**

(7x-1)/4 â€“ 1/3(2x â€“ (1-x)/2) = 10/3

when we expand the given equation,

(7x-1)/4 â€“ (4x-1+x)/6 = 10/3

(7x-1)/4 â€“ (5x-1)/6 = 10/3

By taking LCM for 4 and 6 is 24

((7x-1)6 â€“ (5x-1)4)/24 = 10/3

(42x â€“ 6 â€“ 20x + 4)/24 = 10/3

(22x â€“ 2)/24 = 10/3

After cross-multiplying

22x â€“ 2 = 10(8)

22x â€“ 2 = 80

22x = 80+2

22x = 82

x = 82/22

x = 41/11

Now verify the equation by putting x = 41/11

(7x-1)/4 â€“ 1/3(2x â€“ (1-x)/2) = 10/3

x = 41/11

(7x-1)/4 â€“ (5x-1)/6 = 10/3

(7(41/11)-1)/4 â€“ (5(41/11)-1)/6 = 10/3

(287/11 â€“ 1)/4 â€“ (205/11 â€“ 1)/6 = 10/3

(287-11)/44 â€“ (205-11)/66 = 10/3

276/44 â€“ 194/66 = 10/3

69/11 â€“ 97/33 = 10/3

((69Ã—3) â€“ (97Ã—1))/33 = 10/3

(207 â€“ 97)/33 = 10/3

110/33 = 10/3

10/3 = 10/3

Thus, L.H.S. = R.H.S.,

Hence, the equation is verified.

**Question 22. 0.5(x-0.4)/0.35 â€“ 0.6(x-2.71)/0.42 = x + 6.1**

**Solution:**

0.5(x-0.4)/0.35 â€“ 0.6(x-2.71)/0.42 = x + 6.1

First simplify the given equation

(0.5/0.35)(x â€“ 0.4) â€“ (0.6/0.42)(x â€“ 2.71) = x + 6.1

(x â€“ 0.4)/0.7 â€“ (x â€“ 2.71)/0.7 = x + 6.1

(x â€“ 0.4 â€“ x + 2.71)/0.7 = x + 6.1

-0.4 + 2.71 = 0.7(x + 6.1)

0.7x = 2.71 â€“ 0.4 â€“ 4.27

= -1.96

x = -1.96/0.7

x = -2.8

Now verify the equation by putting x = 5

0.5(x-0.4)/0.35 â€“ 0.6(x-2.71)/0.42 = x + 6.1

x = -2.8

0.5(-2.8 â€“ 0.4)/0.35 â€“ 0.6(-2.8 â€“ 2.71)/0.42 = -2.8 + 6.1

-1.6/0.35 + 3.306/0.42 = 3.3

-4.571 + 7.871 = 3.3

3.3 = 3.3

Thus, L.H.S. = R.H.S.,

Hence, the equation is verified.

**Question 23. 6.5x + (19.5x â€“ 32.5)/2 = 6.5x + 13 + (13x â€“ 26)/2**

**Solution:**

6.5x + (19.5x â€“ 32.5)/2 = 6.5x + 13 + (13x â€“ 26)/2

First rearrange the equation

6.5x + (19.5x â€“ 32.5)/2 â€“ 6.5x â€“ (13x â€“ 26)/2 = 13

(19.5x â€“ 32.5)/2 â€“ (13x â€“ 26)/2 = 13

(19.5x â€“ 32.5 â€“ 13x + 26)/2 = 13

(6.5x â€“ 6.5)/2 = 13

6.5x â€“ 6.5 = 13Ã—2

6.5x â€“ 6.5 = 26

6.5x = 26+6.5

6.5x = 32.5

x = 32.5/6.5

x = 5

Now verify the equation by putting x = 5

6.5x + (19.5x â€“ 32.5)/2 = 6.5x + 13 + (13x â€“ 26)/2

x= 5

6.5(5) + (19.5(5) â€“ 32.5)/2 = 6.5(5) + 13 + (13(5) â€“ 26)/2

32.5 + (97.5 â€“ 32.5)/2 = 32.5 + 13 + (65 â€“ 26)/2

32.5 + 65/2 = 45.5 + 39/2

(65 + 65)/2 = (91+39)/2

130/2 = 130/2

65 = 65

Thus, L.H.S. = R.H.S.,

Hence, the equation is verified.

**Question 24. (3x â€“ 8) (3x + 2) â€“ (4x â€“ 11) (2x + 1) = (x â€“ 3) (x + 7)**

**Solution:**

(3x â€“ 8) (3x + 2) â€“ (4x â€“ 11) (2x + 1) = (x â€“ 3) (x + 7)

First simplify the given equation

9x

^{2}+ 6x â€“ 24x â€“ 16 â€“ 8x^{2}â€“ 4x + 22x + 11 = x^{2}+ 7x â€“ 3x â€“ 219x

^{2}+ 6x â€“ 24x â€“ 16 â€“ 8x^{2}â€“ 4x + 22x + 11 â€“ x^{2}â€“ 7x + 3x + 21 = 09x

^{2}â€“ 8x^{2}â€“ x^{2}+ 6x â€“ 24x â€“ 4x + 22x â€“ 7x + 3x â€“ 16 + 21 + 11 = 0-4x + 16 = 0

-4x = -16

x = 4

Now verify the equation by putting x = 4

(3x â€“ 8) (3x + 2) â€“ (4x â€“ 11) (2x + 1) = (x â€“ 3) (x + 7)

x = 4

(3(4) â€“ 8) (3(4) + 2) â€“ (4(4) â€“ 11) (2(4) + 1) = (4 â€“ 3) (4 + 7)

(12-8) (12+2) â€“ (16-11) (8+1) = 1(11)

4 (14) â€“ 5(9) = 11

56 â€“ 45 = 11

11 = 11

Thus, L.H.S. = R.H.S.,

Hence, the equation is verified.

**Question 25. [(2x+3) + (x+5)]**^{2} + [(2x+3) â€“ (x+5)]^{2} = 10x^{2} + 92

^{2}+ [(2x+3) â€“ (x+5)]

^{2}= 10x

^{2}+ 92

**Solution:**

[(2x+3) + (x+5)]- + [(2x+3) â€“ (x+5)]

^{2}= 10x^{2}+ 92First simplify the given equation

[3x + 8]

^{2}+ [x â€“ 2]^{2}= 10x^{2}+ 92Now apply the formula (a+b)2

9x

^{2}+ 48x + 64 + x^{2}â€“ 4x + 4 = 10x^{2}+ 92After rearranging the equation

9x

^{2}â€“ 10x^{2}+ x^{2}+ 48x â€“ 4x = 92 â€“ 64 â€“ 444x = 24

x = 24/44

x = 6/11

Now verify the equation by putting x = 6/11

[(2x+3) + (x+5)]

^{2}+ [(2x+3) â€“ (x+5)]^{2}= 10x^{2}+ 92x = 6/11

[2(6/11) + 3 + (6/11) + 5]

^{2}+ [2(6/11) + 3 â€“ (6/11) â€“ 5]^{2}= 10(6/11)^{2}+ 92[(12/11 + 3) + (6/11 + 5)]

^{2}+ [(12/11 + 3) â€“ (6/11 + 5)]^{2}= 10(6/11)^{2}+ 92[(12+33)/11 + (6+55)/11]

^{2}+ [(12+33)/11- (6+55)/11]^{2}= 10(6/11)^{2}+ 92[(45/11)+ (61/11)]

^{2}+ [(45/11) â€“ (61/11)]^{2}= 360/121 + 92(106/11)

^{2}+ (-16/11)^{2}= (360 + 11132)/12111236/121 + 256/121 = 11492/121

11492/121 = 11492/121

Thus, L.H.S. = R.H.S.,

Hence, the equation is verified.