help with solving these equations..?

Question

and explain the steps on how to get the answer.
(the letters are variables)


1) 2y+18 = 12-6(y+7)

2) 2(9x - 1) = 99-7(3 - 4x)

3) -x - (13 + 4x) = -3(5 - 9x) +2


thanks guys :)

Answer 1

1.
2y + 18 = 12 - 6(y + 7)
2y + 6 = -6(y + 7) <<< apply distributive property here
2y + 6 = -6y - 42
8y + 6 = - 42
8y = -48
y = -6

Same thing (distributive property) for the other two. Just watch out on 3) for that -(13 + 4x), don't forget that - is -1

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Distributive property is something like this:
a(b + c) = ab + ac
You simply multiply each terms inside the parentheses by what's right outside of it.

Answer 2

2y + 18 = 12-6(y+7)
First distribute the -6 to y + 7
2y + 18 = 12-6(y) + -6(7)
2y + 18 = 12-6y-42
Now, get the Y variables to the left side
2y + 6y + 18 = 12-6y-42+6y
8y + 18 = 12-42
Get the constants on the right side
8y + 18 - 18 = 12-42-18
8y = 12-42-18
Simplify the constants
8y = -48
Divide by 8 on both sides
8y/8 = -48/8
y = -6

2) 2(9x-1)= 99 - 7(3-4x)
Distribute
18x - 2 = 99 - 21+28x
Get the x variable to the right side
-2 = 99 - 21 +10x
Simplify the constants
-2 = 78 + 10 x
Get the constants on the left side
-80 = 10x
Divide by 10
-8 =x

3) -x -(13+4x) = -3(5-9x)+2
Distribute
-x -13-4x = -15 + 27x + 2
Simplify
-5x - 13 = -13+ 27 x
Get the x's on the right side
-13 = -13 +22x
Get the constants on the left
0 = 22x
Divide by 22
0 = x

Answer 3

All these problems are similar, they only have one variable. You are looking for the value of the variable. We need to re-write the equations so that we can end up with the variable on one side of the = sign, and it’s value on the other side of the = sign. So lets break the equations down step by step.

1) 2y+18 = 12 - 6(y+7)

2y+18 = 12 – 6y+42
2y+18 = -6y + 54
8y+18 = 54 (Here I added 6y on this side of the equation, so I also had to add 6y to the other side of the equation. Whatever you do on one side of an equation you will need to do on the other side as well)

8y = 36, Now to let y stand alone we divide both sides by 8 which gives
y = 36/8 which = 4.5,
y = 4.5

2) 2(9x-1) = 99-7(3-4x)

18x -2 = 99-21-28x
18x-2 = 78-28x
18x = 80-28x (I added 2 on both sides of the equation here and got rid of the –2 from the left side of the equation)

46x = 80 ( I added 28x here in order to get rid of the –28x on the right side of the equation, now all my x’s are on the left side and some value is on the right, so we are now able to solve for x by dividing both sides by 46 )
x=80/46,
x=1.739


3) -x - (13 + 4x) = -3(5 - 9x) +2

-x – 13 – 4x = -15 +27x +2
-5x –13 = -13 +27x
-5x = 27x
This problem doesn’t resolve. Either the problem was copied down incorrectly or I have made a mistake that I’m not seeing, or it was meant to be given as a problem that is not solvable.

Answer 4

1) 2y + 18 = 12 - 6(y + 7) -> : 2

y + 9 = 6 - 3(y + 7)

y + 3(y + 7) = 6 - 9

y + 3y + 21 = -3

4y = -3 -21 = -24

y = -24/4 = -6

2) 2(9x - 1) = 99 - 7(3 - 4x)

18x - 2 = 99 - 21 + 28

18x = 106 + 2

x = 6

3) -x - (13 + 4x) = -3(5 - 9x) + 2

-x - 13 - 4x = -15 + 27x + 2

-27 x - 5x = -13 + 13

x = 0

You are welcome!

Answer 5

Hello Softballa...

1.) 2Y + 18 = 12 - 6 (y + 7)

2Y + 18 = 12 - 6Y - 42 = - 6Y -30

2Y = -6Y -48

8Y = -48 and Y = -6

2.) 2(9X -1) = 99 - 7(3 - 4X)

18X -2 = 99 - 21 + 28X = 78 + 28X

18X = 78 + 2 + 28X

18X - 28X = 80

- 10X = 80 and X = - 8

3.) -X - (13 + 4X) = - 3 (5 - 9X) +2

-X - 13 - 4X = - 15X + 27X + 2

-5X - 13 = 12X + 2

-13 -2 -5X = 12X

-15 -5X = 12 X

-15 = 17X

X = - 15/17

Regards,
Zahbudar

Answer 6

1) 2y+18 = 12-6(y+7)
2y+18=12-6y-42
2y+6y=12-42-18
8y=-48=y=-6

2) 2(9x - 1) = 99-7(3 - 4x)
18x-2=99-21+28x
-10x=99-21+2
-10x=80
x=-8

3) -x - (13 + 4x) = -3(5 - 9x) +2
-x-13-4x=-15+27x+2
-5x-13=27x-13
-32x=0
x=0

Answer 7

1) 2y+18=12-6y-42
2y+6y=-18+12-42
8y=-48
y=-6

2)18x-2=99-21+28x
18x-28x=99-21+2
-10x=80
x=-8

3) -x-13-4x=-15+27x+2
-x-4x-27x=13-15+2
-32x=0
x=0

Answer 8

1) 2y+18=12-6(y+7)
2y=12-6y-42-18
8y=-48
y=-6

2) 2(9x-1) = 99-7(3-4x)
18x - 2 = 99 - 21+28x
-10x=80
x=-8

k... can't do anymore math.. lol i showed the work for them so u cud understand wat i was doing and maybe finish the last one on ur own...

Answer 9

1).2y+18=12-6(y+7)