Answers:
1. b = - 6
2. z = -7.5
3. c = 5
4. s = -38
5. w = 12
6. m = -(12/7)
7. k = 88
8. x = -10
9. t = -7.5
10. d = 0.3
11. "a" can be any value (Infinite solutions)
12. No solution for "n"
Solution:
1. -7(b+16)=7(b-4)
Dividing both sides of the equation by 7:
-7(b+16)/7=7(b-4)/7
-(b+16)=b-4
-b-16=b-4
-b-16+b+4=b-4+b+4
-12=2b
2b=-12
2b/2=-12/2
b=-6
Checking the solution:
-7(b+16)=7(b-4)
-7(-6+16)=7(-6-4)
-7(10)=7(-10)
-70=-70 Ok
2. 9-z=3z+39
9-z+z-39=3z+39+z-39
-30=4z
4z=-30
4z/4=-30/4
z=-7.5
Checking the solution:
9-z=3z+39
9-(-7.5)=3(-7.5)+39
9+7.5=-22.5+39
16.5=16.5 Ok.
3. 12c-5c=4c+15
7c=4c+15
7c-4c=4c+15-4c
3c=15
3c/3=15/3
c=5
Checking the solution:
12c-5c=4c+15
12(5)-5(5)=4(5)+15
60-25=20+15
35=35 Ok
4. 40-5s=-2(-1+3s)
40-5s=(-2)(-1)+(-2)(3s)
40-5s=2-6s
40-5s-40+6s=2-6s-40+6s
s=-38
Checking the solution:
40-5s=-2(-1+3s)
40-5(-38)=-2(-1+3(-38))
40+190=-2(-1-114)
230=-2(-115)
230=230 Ok
5. 2.8w+5.3=3.3w-0.7
2.8w+5.3-2.8w+0.7=3.3w-0.7-2.8w+0.7
6=0.5w
0.5w=6
0.5w/0.5=6/0.5
w=12
Checking the solution:
2.8w+5.3=3.3w-0.7
2.8(12)+5.3=3.3(12)-0.7
33.6+5.3=39.6-0.7
38.9=38.9 Ok
6. 4(m+9)=3(8-m)
(4)(m)+(4)(9)=(3)(8)+(3)(-m)
4m+36=24-3m
4m+36-36+3m=24-3m-36+3m
7m=-12
7m/7=-12/7
m=-12/7
Checking the solution:
4(m+9)=3(8-m)
4(-12/7+9)=3(8-(-12/7))
4(-12+7(9))/7=3(8+12/7)
4(-12+63)/7=3(7(8)+12)/7
4(51)/7=3(56+12)/7
204/7=3(68)/7
204/7=204/7 Ok
7. (1/8)k+32=(1/2)k-1
(1/8)k+32-32-(1/2)k=(1/2)k-1-32-(1/2)k
(1/8-1/2)k=-33
[(1-4(1))/8]k=-33
[(1-4)/8]k=-33
[(-3)/8]k=-33
(-3/8)k=-33
(-1)(-3/8)k=(-1)(-33)
(3/8)k=33
k=8(33)/3
k=264/3
k=88
Checking the solution:
(1/8)k+32=(1/2)k-1
(1/8)(88)+32=(1/2)(88)-1
(1)(88)/8+32=(1)(88)/2-1
88/8+32=88/2-1
11+32=44-1
43=43 Ok
8. (3/4)x-x=-(1/4)(2x+10)
Multiplying both sides of the equation by 4:
4(3/4)x-4x=-(4/4)(2x+10)
3x-4x=-1(2x+10)
-x=(-1)(2x)+(-1)(10)
-x=-2x-10
-x+2x=-2x-10+2x
x=-10
Checking the solution:
(3/4)x-x=-(1/4)(2x+10)
(3/4)(-10)-(-10)=-(1/4)(2(-10)+10)
-30/4+10=-(1/4)(-20+10)
-7.5+10=-(1/4)(-10)
2.5=10/4
2.5=2.5 Ok
9. 9(t+1)=5(t-4)-1
(9)(t)+(9)(1)=(5)(t)+(5)(-4)-1
9t+9=5t-20-1
9t+9=5t-21
9t+9-9-5t=5t-21-9-5t
4t=-30
4t/4=-30/4
t=-7.5
Checking the solution:
9(t+1)=5(t-4)-1
9(-7.5+1)=5(-7.5-4)-1
9(-6.5)=5(-11.5)-1
-58.5=-57.5-1
-58.5=-58.5 Ok
10. 3d+1.1=2.3-d
3d+1.1-1.1+d=2.3-d-1.1+d
4d=1.2
4d/4=1.2/4
d=0.3
Checking the solution:
3d+1.1=2.3-d
3(0.3)+1.1=2.3-0.3
0.9+1.1=2.0
2.0=2.0 Ok
11. -7(a+2)+15=1-7a
(-7)(a)+(-7)(2)+15=1-7a
-7a-14+15=1-7a
-7a+1=1-7a
-7a+1-1+7a=1-7a-1+7a
0=0
"a" can be any value (Infinite solutions)
Checking the solution: For example a=0
-7(a+2)+15=1-7a
-7(0+2)+15=1-7(0)
-7(2)+15=1-0
-14+15=1
1=1 Ok
12. 6(3n-1)=2(9n+4)
(6)(3n)+(6)(-1)=(2)(9n)+(2)(4)
18n-6=18n+8
18n-6+6-18n=18n+8+6-18n
0=14 It's not possible, because 0 is different to 14, then there is no solution for "n".
-7(b + 16) = 7(b - 4)
Solution:
-7(b + 16) = 7(b - 4)
= -7b - 112 = 7b - 28
= -112 + 28 = 7b + 7b
= -84 = 14b
= b = -84/14
= b = -6
Rechecking:
-7(b + 16) = 7(b - 4)
= -7(-6 + 16) = 7(-6 - 4)
= -70 = -70
Hence b = -6
Part 2.
9 - z = 3z+ 39
Solution:
9 - z = 3z + 39
= 3z + z = 39 - 9
= 4z = 30
= z = 30/4= 7.5
= z = 7.5
Rechecking:
9-z = 3z+39
9-(-7.5) = 3(-7.5)+39
9+7.5 = -22.5+39
16.5 = 16.5
Hence z = 7.5
12c - 5c = 4c + 15
Solution:
12c - 5c = 4c + 15
= 7c - 4c = 15
= 3c = 15
= c = 15/3
= c = 5
Rechecking:
12c - 5c = 4c + 15
= 12(5)-5(5 )= 4(5)+15
= 60-25 = 20+15
= 35 = 35
Hence proved c = 5
40 - 5s = -2 (-1 + 3s)
Solution:
40 - 5s = -2 (-1 + 3s)
= 40 - 5s = 2 - 6s
= 6s - 5s = 2 - 40
= s = -38
Rechecking:
40 - 5s = -2 (-1 + 3s)
40 - 5(-38)=-2(-1 + 3(-38))
= 40 + 190 = -2(-1-114)
= 230 = -2(-115)
= 230 = 230
Hence proved s = -38
2.8w + 5.3 = 3.3w - 0.7
Solution:
2.8w + 5.3 = 3.3w - 0.7
= 2.8w - 3.3w = -0.7 - 5.3
= -0.5w = - 6.0
= w = -6.0/-0.5
= w = 12
Rechecking:
2.8w + 5.3 = 3.3w - 0.7
= 2.8(12) + 5.3 = 3.3(12) - 0.7
= 33.6 + 5.3 = 39.6 - 0.7
= 38.9 = 38.9
Hence proved w = 12
4(m+9) = 3(8-m)
Solution:
= 4m + 36 = 24 - 3m
= 36 - 24 = -3m - 4m
= 12 = -7m
= m = 12/-7 = 1.714...
As the m is equal to -12/7 which is equal to a fraction value.
So we will take m = -12/7
Rechecking:
4(m+9) = 3(8-m)
= 4(-12/7+9) = 3(8-(-12/7))
= 4(-12+7(9))/7 = 3(8+12/7)
= 4(-12+63)/7 = 3(7(8)+12)/7
= 4(51)/7 = 3(56+12)/7
= 204/7 = 3(68)/7
= 204/7 = 204/7
Hence proved m = -12/7
(1/8)k + 32 = (1/2)k - 1
Solution:
(1/8)k + 32 = (1/2)k - 1
= 1k/8 + 32 = 1k/2 - 1
= (1/8)k - (1/2)k = -1 - 32
= ((1 - 4)/8)k = -33
= (-3/8)k=-33
= k = -33 * -8/3
= k = 88
Rechecking:
(1/8)k + 32 = (1/2)k - 1
= (1/8)(88)+32=(1/2)(88)-1
= (1)(88)/8+32=(1)(88)/2-1
= 88/8+32=88/2-1
= 11+32=44-1
= 43=43
Hence proved k = 88
Part 8.
(3/4)x - x= -(1/4) (2x + 10)
Solution:
(3/4)x - x= -(1/4) (2x + 10)
= (3/4)x - x= -1/2x - 2.5
= (3/4)x - x + (1/2)x = -2.5
= (3/4 - 1 + 1/2)x = -2.5
= -0.25 x = -2.5
= x = -2.5/0.25
= x = 10
Rechecking:
(3/4)x - x= -(1/4) (2x + 10)
(3/4)(-10)-(-10)=-(1/4)(2(-10)+10)
= -30/4 + 10 = -(1/4)(-20+10)
= -7.5 + 10 = -(1/4)(-10)
= 2.5 = 10/4
= 2.5 = 2.5
Hence proved x = 10
9(t+1) = 5(t-4) - 1
Solution:
9(t+1) = 5(t-4) - 1
= 9t +9 = 5t - 20 - 1
= 9t - 5t = -20 - 1 - 9
= 4t = -30
= t = -30/4
= t = -7.5
Rechecking the solution:
9(t+1) = 5(t-4) - 1
= 9(-7.5+1 ) = 5(-7.5-4) - 1
= 9(-6.5)=5(-11.5)-1
= -58.5 = -57.5 - 1
= -58.5 = -58.5
Hence proved t = -7.5
3d + 1.1 = 2.3 - d
Solution:
3d + 1.1 = 2.3 - d
= 3d + d = 2.3 - 1.1
= 4d = 1.2
= d = 1.2/4
= d = 0.3
Rechecking the answer:
3d + 1.1 = 2.3 - d
= 3(0.3) + 1.1=2.3 - 0.3
= 0.9 + 1.1 = 2.0
= 2.0 = 2.0
Hence proved d = 0.3
-7(a+2) + 15= 1 - 7a
Solution:
-7(a+2) + 15= 1 - 7a
= -7a -14 + 15 = 1 - 7a
= -7a + 7a = 1 + 14 - 15
= 0 = 15 - 15
= 0 = 0
Here the value of a is an infinite solution. As the value of a is infinite so there is no solution of a.
6(3n - 1) = 2(9n + 4)
Solution:
6(3n - 1) = 2(9n + 4)
= 18n - 6 = 18n + 8
= 18n - 18n = 8 + 16
= 0 = 16 ( wrong equation)
The solution came is 0 = 16 which is not possible. 0 and 16 are not equal. Hence the given equation is not correct equation.
There is something wrong in equation.
