Question

1) 3(b-1)-1=8(b-1)-6 2) 5(x-6)-2=(x-7)-6 3) 28+5a=44+a 4) 15k+40=29k-2 5) 51+3p=57+p 6) -50(-3m+10)=-200 7) -62(2n+22)=-1860

Answer 1

3b-3-1=8b-8-6

-5b=-14+4

-5b=-10

b=-10÷(-5)

b=2

Answer 2

1) 3(b-1)-1=8(b-1)-6

3b-3-1=8b-8-6

3b-4=8b-14

3b-8b=-14+4

-5b=-10

b=2

2) 5(x-6)-2=(x-7)-6

5x-30-2=x-7-6

5x-32=x-13

5x-x=-13+32

4x=19

x=4,75

3) 28+5a=44+a

5a-a=44-28

4a=16

a=4

4) 15k+40=29k-2

15k-29k=-2-40

-14k=-42

k=3

5) 51+3p=57+p

3p-p=57-51

2p=6

p=3

6) -50(-3m+10)=-200

150m-500=-200

150m=300

m=2

7) -62(2n+22)=-1860

-124n+1364=-1860

-124n=−3224

n=26

Answer 3

Let's solve the given equations one by one:

1. 3(b-1)-1=8(b-1)-6

Let's simplify the equation:

3b - 3 - 1 = 8b - 8 - 6

Combine like terms:

3b - 4 = 8b - 14

Rearrange the terms:

8b - 3b = -14 + 4

5b = -10

Divide both sides by 5:

b = -2

2. 5(x-6)-2=(x-7)-6

Expand and simplify the equation:

5x - 30 - 2 = x - 7 - 6

Combine like terms:

5x - 32 = x - 13

Subtract x from both sides:

5x - x - 32 = -13

4x - 32 = -13

Add 32 to both sides:

4x = 19

Divide both sides by 4:

x = 19/4 or 4.75

3. 28 + 5a = 44 + a

Subtract a from both sides:

28 + 4a = 44

Subtract 28 from both sides:

4a = 16

Divide both sides by 4:

a = 4

4. 15k + 40 = 29k - 2

Subtract 15k from both sides:

40 = 14k - 2

Add 2 to both sides:

42 = 14k

Divide both sides by 14:

k = 3

5. 51 + 3p = 57 + p

Subtract p from both sides:

51 + 2p = 57

Subtract 51 from both sides:

2p = 6

Divide both sides by 2:

p = 3

6. -50(-3m + 10) = -200

Distribute -50 to the terms inside the parentheses:

150m - 500 = -200

Add 500 to both sides:

150m = 300

Divide both sides by 150:

m = 2

7. -62(2n + 22) = -1860

Distribute -62 to the terms inside the parentheses:

-124n - 1364 = -1860

Add 1364 to both sides:

-124n = -496

Divide both sides by -124:

n = 4

So, the solutions to the given equations are:

1. b = -2
2. x = 4.75
3. a = 4
4. k = 3
5. p = 3
6. m = 2
7. n = 4