Solve for the solution set of the following equations.?

Question

Hi! I'm 2nd Year High School from the Philippines and I got problems on Solution Set! Give me the answers and tell me or explain to me how you got it step by step! Thanks alot ><
1.) 8y - 35 = 3y
2.) 6x + 3 = 2x + 11
3.) 5y - 2 = 28 - y
4.) -18s + 6s + 2s = -9s + 15
5.) 7(2a - 1) = 21
6.) 9 = 3 (5x - 2)
7.) 2(3 + 4m) - 9 = 45
8.) -2 (r - 1) + 7 = 3 (r + 5)
9.) 7 - 2x - ( - x + 7 ) = 3 + x - (x - 3)
10.) z - 6 (3z + 4) = 5[2z + (3z + 4) - 22]

Once again! Thanks alot!

Answer 1

8y - 35 = 3y

8y - 35 - 3y = 3y - 3y

5y - 35 = 0

5y - 35 + 35 = 0 + 35

5y = 35

5y / 5 = 35 / 5

y = 35 / 5

y = 7
- - - - - - - -

6x + 3 = 2x + 11

6x + 3 - 2x = 2x + 11 - 2x

4x + 3 = 11

4x + 3 - 3 = 11 - 3

4x = 8

4x /4 = 8 / 4

x = 8 / 4

x = 2
- - - - - - - - - -

5y - 2 = 28 - y

5y - 2 + y = 28 - y + y

6y - 2 = 28

6y - 2 + 2 = 28 + 2

6y = 30

6y / 6 = 30 / 6

y = 30/6

y = 5

- - - - - - - -

- 18s + 6s + 2s = - 9s + 15

- 18x + 8s = - 9x + 15

- 10s = - 9s + 15

- 10s + 9s = - 9s + 15 + 9s

- s = 15

- (- 1)(s) = - 1(15)

- (- s) = - 15

s = - 15

- - - - - - - - - -s-

Answer 2

1. 8y - 35 = 3y
8y - 35 = 3y
8y-3y-35+35 =3y-3y+35
5y=35
5 y/5=35/5
y = 7

2. 6x + 3 = 2x + 11
6x-2x+3 = 2x-2x+11
4x+3-3 = 11-3
6x-2x=11-3
4x = 8
4x/4 = 8/4
x=2

3. 5y - 2 = 28 - y
5y+y-2 = 28 -y+y
6y-2 = 28
6y -2+2 = 28 +2
6y = 30
6y/6 = 30/6
y = 5

4. -18s + 6s + 2s = -9s + 15
-18s+6s+2s +9s =15
-s = 15
-s/(-1)= 15/(-1)
s = -15

5. 7(2a - 1) = 21
14a-7 =21
14a-7+7 = 21+7
14a =28
14a/14 = 28/14
a = 2

6. 9 = 3 (5x - 2)
9 =15x-6
15x-6 = 9
15x-6+6 = 9+6
15x =15
15x/15 = 15/15
x = 1

7. 2(3 + 4m) - 9 = 45
6 + 8m- 9 =45
8m - 3 = 45
8m-3+3 = 45+3
8m = 48
8m/8 = 48/8
m = 6

8. -2 (r - 1) + 7 = 3 (r + 5)
-2r + 2 +7 = 3r +15
-2r + 9 = 3r +15
-2r-3r + 9 = 3r-3r +15
-5r + 9 = 15
-5r + 9 - 9 =15 -9
-5r = 6
-5r/-5 = 6/-5
r = -6/5

9. 7 - 2x - ( - x + 7 ) = 3 + x - (x - 3)
7 - 2x + x -7 = 3 + x -x + 3
- x = 6
-x/(-1) = 6/(-1)
x = -6


10. z - 6 (3z + 4) = 5[2z + (3z + 4) - 22]
z- 18z -24 = 5(5z-18)
z - 18z -24 = 25z-90
-17z-24 = 25z - 90
-17z-25z -24 = 25z-25z-90
-42z - 24 = -90
-42z - 24 +24 = -90 + 24
- 42 z = -66
-42z/(-42) = -66/(-42)
z = 66/42
z = (-66/6)/[(-42)/6]
z = 11/7

Answer 3

1.) 8y - 35 = 3y
subtract 3y from both sides
5y-35=0
add 35 to both sides
5y=35
divide both sides by 5
y=7

2.) 6x + 3 = 2x + 11
subtract 2x from both sides
4x+3=11
subtract 3 from both sides
4x=8
divide both sides by 4
x=2

3.) 5y - 2 = 28 - y
add 1y to both sides
6y-2=28
add 2 to both sides
6y=30
divide both sides by 6
y=5

4.) -18s + 6s + 2s = -9s + 15
combine s values on left side of the equation
-10s=-9s+15
add 9s to both sides
-s = 15
divide both sides by -1
s = -15

5.) 7(2a - 1) = 21
distribute the 7
14a-7 =21
add 7 to both sides
14a = 28
divide both sides by 14
a = 2

6.) 9 = 3 (5x - 2)
distribute the 3
9 = 15x -6
add 6 to both sides
15 = 15x
divide both sides by 15
1 = x
x = 1

7.) 2(3 + 4m) - 9 = 45
distribute the 2
6 + 8m -9 =45
combine like terms
8m - 3 = 45
add 3 to both sides
8m = 48
divide both sides by 8
m = 48/8
m=24/4
m=12/2
m=6

8.) -2 (r - 1) + 7 = 3 (r + 5)
distribute the -2
-2r+1+7 = 3(r+5)
combine like terms
-2r +8 = 3(r+5)
distribute the 3
-2r+8 = 3r +15
subtract 8 from both sides
-2r = 3r +7
suntract 3r from both sides
-5r = 7
divide both side by -5
r = -5/7

9.) 7 - 2x - ( - x + 7 ) = 3 + x - (x - 3)
distribute the - signs in front of the ()
7 - 2x +x -7 = 3 + x - x +3
combine like terms
-x = 6
divide both sides by -1
x = 6

10.) z - 6 (3z + 4) = 5[2z + (3z + 4) - 22]
distribute the -6
z -18z -24 = 5[2z +(3z+4)-22]
distribute the 5, combine the z terms on the left hand side
-17z - 24 = 10z + 5(3z+4) -110
distribute the 5
-17z - 24 = 10z + 15z+20 -110
combine like terms on the right hand side
-17z -24 = 25z -90
add 17z to both sides
-24 = 42z -90
add 90 to both sides
66 = 42z
divide both sides by 42
66/42 = z
z = 66/ 42
z = 33/ 21
z = 11/7

Answer 4

1 8y-3y=35 5y=35 y=7
2 6x-2x=-3+11 4x=8 x=2
3 5y+y=28+2 6y=30 y=5
thanks for practice i am from 4th standard

Answer 5

permit x = y^2 - 4. we've x^2 + 5x - 50 = 0 (x + 10)(x - 5) = 0 x = -10 or x = 5. when you consider that x = y^2 - 4, we've y^2 - 4 = -10 or y^2 - 4 = 5 y^2 = -6 or y^2 = 9 y = +-i*sqrt(6) or y = +-3. The 4 suggestions for y are +-i*sqrt(6), +-3. Lord bless you at present!