Question

Please help 1-12!!!!

Answer 1

Part 1.

-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

Part 3.

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

Part 4.

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

Part 5.

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

Part 6.

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

Part 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

Part 9.

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

Part 10.

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

Part 11.

-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.

Part 12.

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.

Answer 2

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".