PAGE NO 9.11:
Question 1:
Solve each of the following equation and also check your result in each case:
= 3x 10
ANSWER:
= 3x 10
or 2x + 5 = 9 x −30
or 9 x −2x = 5 + 30
or 7x = 35
or x = 35/7
or x = 5
Verification:L.H.S. = = 15/3 = 5
R.H.S. = 15−10 = 5
∴ L.H.S. = R.H.S. for x = 5.
PAGE NO 9.11:
Question 2:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 2a−16 = 3a−9
or 3a−2a = −16 + 9
or a = −7
Verification:
L.H.S. = = 5
R.H.S. = = 5
∴ L.H.S. = R.H.S. for a = −7
PAGE NO 9.11:
Question 3:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 77y + 22 = 30y−25
or 77y−30y = −25−22
or 47y = −47
or y = −47/47 = −1
Verification:L.H.S. =
R.H.S. =
∴ L.H.S. = R.H.S. for y = −1
PAGE NO 9.11:
Question 4:
Solve each of the following equation and also check your result in each case:
x −2x + 2−16/3x + 5 = 3−7/2x
ANSWER:
x −2x + 2−16/3x + 5 = 3−7/2x
or −38 x + 42 = 18−21 x
or −21 x + 38 x = 42−18
or 17x = 24
or x = 24/17
Check:L.H.S. = 24/17 − 2 × 24/17 + 7 − 16/3 × 24/17 = −33/17
R.H.S. = 3− 7/2 × 24/17 = −33/17
∴ L.H.S. = R.H.S. for x = 24/17
PAGE NO 9.11:
Question 5:
Solve each of the following equation and also check your result in each case:
1/2x + 7x −6 = 7x + 1/4
ANSWER:
1/2x + 7x −6 = 7x + 1/4
or 1/2x + 7x −7x = 1/4 + 6
or x/2 =
or x/2 = 25/4
or x = 25/2
Check:L.H.S. = 12×25/2 + 7×25/26 = 35/14
R.H.S. = 7×25/2 + 1/4 = 35/14
∴ L.H.S. = R.H.S. for x = 25/2
PAGE NO 9.11:
Question 6:
Solve each of the following equation and also check your result in each case:
3/4 x + 4 x = 7/8 + 6 x −6
ANSWER:
3/4 x + 4 x = 7/8 + 6 x −6
or 3/4 x −2x = 7/8−6
or−5 x/ 4 = −41/8
or −40 x = −16/4
or x = −164/−40 = 41/10
Check:
L.H.S. = 3/4×41/10 + 4×41/10 = 123/40 + 164/10 =
R.H.S. = 7/8 + 6×41/10  6 = 7/8 + 246/10  6 =
∴ L.H.S. = R.H.S. for x = 41/10
PAGE NO 9.11:
Question 7:
Solve each of the following equation and also check your result in each case:
7/2 x −5/2 x = 20/3x + 10
ANSWER:
7/2 x −5/2 x = 20/3x + 10
or 40 x + 60 = 6 x
or 34 x = −60
or x = −60/34
= −30/17
Check:
L.H.S. = 7/2×−30/17−5/2× −30/17 = −30/17
R.H.S. = 20/3×−30/17 + 10 = −30/17
∴L.H.S. = R.H.S. for x = −30/17
PAGE NO 9.11:
Question 8:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 18 x + 9 = 14 x −6
or 18 x −14 x = −6−9
or 4 x = −15
or x = −15/4
Check:
L.H.S. =
R.H.S. =
∴ L.H.S. = R.H.S. for x = −15/4
PAGE NO 9.11:
Question 9:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 12a + 5 = 6a + 7
or 6a = 7−5
or a = 2/6 = 1/3
Check:
L.H.S. = = 1/3 + 11/6 = 9/6 = 3/2
R.H.S. = 1/3 + 7/6 = 9/6 = 3/2
∴ L.H.S. = R.H.S. for a = 1/3
PAGE NO 9.11:
Question 10:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 3x + 3 = 10−2x
or 5 x = 10−3
or x = 7/5
Check:
L.H.S. =
R.H.S. =
∴ L.H.S. = R.H.S. for x = 7/5
PAGE NO 9.11:
Question 11:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 4 x −8 = 3x + 6
or x = 14
L.H.S. = = 21/213/2 = 8/2 = 4
R.H.S. =
∴ L.H.S. = R.H.S. for x = 14
PAGE NO 9.11:
Question 12:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 85 x + 15 = 12x −36
or 73x = −51
or x = −51/73
Check:L.H.S. = = 255/219  124292 = 5473
R.H.S. =
∴ L.H.S. = R.H.S. for x = −51/73
PAGE NO 9.11:
Question 13:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 7x −35 = −8 x + 40
or 15 x = 75
or x = 75/15 = 5
Check:
L.H.S. =
R.H.S. =
∴ L.H.S. = R.H.S. for x = 5
PAGE NO 9.11:
Question 14:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 8−16 x = 98−7x
or −16 x + 7x = 98−8
or x = −90/9
= −10
Check:L.H.S. = = 34 = 1
R.H.S. =
∴ L.H.S. = R.H.S. for x = −10
PAGE NO 9.11:
Question 15:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 51 x + 45 = 504
or 51 x = 504−45
or x = 459/51 = 9
Thus, x = 9 is the solution of the given equation.
Check:Substituting x = 9 in the given equation, we get:
L.H.S. = = 88/2−9 + 7/7 = 44−9 + 1 = 36
R.H.S. = 36
∴ L.H.S. = R.H.S. for x = 9.
PAGE NO 9.11:
Question 16:
Solve each of the following equation and also check your result in each case:
0.18(5 x − 4) = 0.5 x + 0.8
ANSWER:
0.18(5 x −4) = 0.5 x + 0.8
or 0.9 x −0.72 = 0.5 x + 0.8
or 0.9 x −0.5 x = 0.8 + 0.72
or 0.4 x = 1.52
or x = 1.52/0.4
or x = 3.8
Thus, x = 3.8 is the solution of the given equation.
Check:Substituting x = 3.8 in the given equation, we get:
L.H.S. = 0.18(5×3.8−4) = 0.18×15 = 2.7
R.H.S. = 0.5×3.8 + 0.8 = 2.7
∴ L.H.S. = R.H.S. for x = 3.8.
PAGE NO 9.11:
Question 17:
Solve each of the following equation and also check your result in each case:
2/3x −3/2x = 1/12
ANSWER:
2/3x −3/2x = 1/12
or 6 x = −60
or x = −60/6
or x = −10
Thus, x = −10 is the solution of the given equation.
Check:Substituting x = −10 in the given equation, we get:
L.H.S. =
R.H.S. = 1/12
∴ L.H.S. = R.H.S. for x = −10.
PAGE NO 9.11:
Question 18:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 61 x + 36 = 6(8 x + 19) [Multiplying both sides by 108]
or 61 x + 36 = 48 x + 114
or 61 x −48 x = 114−36
or 13x = 78
or x = 78/13
or x = 6
Thus, x = 6 is the solution of the given equation.
Check:Substituting x = 6 in the given equation, we get:
L.H.S. =
R.H.S. =
∴ L.H.S. = R.H.S. for x = 6.
PAGE NO 9.12:
Question 19:
Solve each of the following equation and also check your result in each case:
ANSWER:
[Multiplying both sides by 3]
or 45−42x = 75−70 x [After cross multiplication]
or 70 x −42x = 75−45
or 28 x = 30
or x = 30/28
or x = 15/14
Thus, x = 15/14 is the solution of the given equation.
Check:Substituting x = 15/14 in the given equation, we get:
L.H.S. =
R.H.S. =
∴ L.H.S. = R.H.S. for x = 15/14
PAGE NO 9.12:
Question 20:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 39 x + 23 = 62 [Multiplying both sides by 3]
or 39 x = 62−23
or x = 39/39
or x = 1
Thus, x = 1 is the solution of the given equation.
Check:Substituting x = 1 in the given equation, we get:
L.H.S. =
R.H.S. =
∴ L.H.S. = R.H.S. for x = 1.
PAGE NO 9.12:
Question 21:
Solve each of the following equation and also check your result in each case:
ANSWER:
or 11 x −1 = 40 [Multiplying both sides by 12]
or 11 x = 40 + 1
or x = 41/11
Thus, x = 41/11 is the solution of the given equation.
Check:Substituting x = 41/11 in the given equation, we get:
L.H.S. =
R.H.S. = 10/3
∴ L.H.S. = R.H.S. for x = 41/11
PAGE NO 9.12:
Question 22:
Solve each of the following equation and also check your result in each case:
= x + 6.1
ANSWER:
= x + 6.1
or −0.4 + 2.71 = 0.7x + 4.27
or 0.7x = 2.71−0.4−4.27
or x = −1.96/0.7 = −2.8
Thus, x = −2.8 is the solution of the given equation.
Check:
Substituting x = −2.8 in the given equation, we get:
L.H.S. == −4.571 + 7.871 = 3.3
R.H.S. = −2.8 + 6.1 = −3.3
∴ L.H.S. = R.H.S. for x = −2.8
PAGE NO 9.12:
Question 23:
Solve each of the following equation and also check your result in each case:
6.5 x + = 6.5 x + 13 +
ANSWER:
6.5 x + = 6.5 x + 13 +
or 6.5 x −6.5 = 26 [After cross multiplication]
or 6.5 x = 26 + 6.5
or x = 32.5/6.5 = 5
Thus, x = 5 is the solution of the given equation.
Check:
Substituting x = 5 in the given equation, we get:
L.H.S. = 6.5×5 +
R.H.S. = 6.5×5 + 13 +
∴ L.H.S. = R.H.S. for x = 5.
PAGE NO 9.12:
Question 24:
Solve each of the following equation and also check your result in each case:
(3x − 8)(3x + 2) − (4 x − 11)(2x + 1) = ( x − 3)( x + 7)
ANSWER:
(3x −8)(3x + 2)−(4 x −11)(2x + 1) = ( x −3)( x + 7)
or 9 x² + 6 x −24 x −16−8 x²−4 x + 22x + 11
= x² + 7x −3x −21
or x²−5 = x² + 4 x −21
or 4 x = −5 + 21
or x = 16/4 = 4
Thus, x = 4 is the solution of the given equation.
Check:
Substituting x = 4 in the given equation, we get:
L.H.S. = (3×4−8)(3×4 + 2)−(4×4−11)(2×4 + 1) = 4×14−5×9 = 11
R.H.S. = (4−3)(4 + 7) = 11
∴ L.H.S. = R.H.S. for x = 4.
PAGE NO 9.12:
Question 25:
Solve each of the following equation and also check your result in each case:
[(2x + 3) + ( x + 5)]^{2} + [(2x + 3) − ( x + 5)]^{2} = 10 x² + 92
ANSWER:
[(2x + 3) + ( x + 5)]² + [(2x + 3)−( x + 5)]²
= 10 x² + 92
or (3x + 8)² + ( x −2)²
= 10 x² + 92
or 9 x² + 48 x + 64 + x²−4 x + 4
= 10 x² + 92 [ (a + b)² = a² + b² + 2ab and (a−b)² = a² + b²−2ab ]
or 10 x²−10 x² + 44 x = 92−68
or x = 24/44
or x = 6/11
Thus, x = 6/11 is the solution of the given equation.
Check:
Substituting x = 6/11 in the given equation, we get:
L.H.S. = [(2 × 6/11 + 3) + (6/11 + 5)]^{2} + [(2 × 6/11 + 3)−(6/11 + 5)]^{2 }
= [(45/11) + (61/11)]^{2} + [(45/11)−(61/11)]^{2 }
= (106/11)^{2} + (−16/11)^{2 }
= 11492/121
R.H.S. =
∴ L.H.S. = R.H.S. for x = 6/11
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