math question. pre-cal. 10points.?

Question

x = 2, y = -3
2x^2 + 3xy

and

x/3 + 1 = x-4

and

2x + 3 = 3x + ____ x=-8
what number goes in the blank?

please explain how u got the answer. thanks. please!! 10points!

Answer 1

1.) 2x² + 3xy
= 2(2)² + 3(2)(-3) ==> Just put the number into the variable
= 2(4) + 3(-6)
= 8 + (-18)
= -10

2.) Are you meant x over 3 + 1 or x over 3? I'm took both.
x / 3 + 1 = x - 4 ==> I'm doing x over 3 + 1
x = (x - 4)(3 + 1) ==> Expand by using F.O.I.L method
x = 4x - 16
x - 4x = -16 ==> Reorder and combine like terms
-3x = -16
x = -16 / -3
x = 5.333 ==> 3d.p
OR
(x / 3) + 1 = x - 4 ==> Now I'm doing x over 3
x + 1 = 3(x - 4) ==> Expand the bracket
x + 1 = 3x - 12
x - 3x = -12 - 1 ==> Reorder and combine like terms
-2x = -13
x = -13 / -2
x = 7.5

3.) Are you meant the solution of x is -8?
Lets the number goes in the blank, n
2x + 3 = 3x + n
2x - 3x = -3 + n ==> Reorder and combine like terms
-x = -3 + n ==> Replace x by -8
-(-8) = -3 + n
8 = -3 + n
n = 8 + 3
n = 11
-----------------------------------------------------------------------------------
REMEMBER
When any number brought to the other side, their sign must be changed. For example when -7 is brought to other side, it's becoming +7.

Answer 2

The first one, it looks like you just plug in the numbers. So...

2(2)^2 + 3(2)(-3) = -10

The second one, you have to use a bit of algebra....

(x/3) +1 = x-4
Times both sides by 3
x+3 = 3x-12
subtract 3 from both sides
x = 3x-15
subtract 3x from both sides
-2x = -15
divide both sides by -2
x = 7.5


The third problem is very similar.....
2x + 3 = 3x + y (y = the number in the blank)
Now, plug in x
2(-8) + 2 = 3(-8) + y
-16 +2 = -24 + y
-14 = -24 +y
now, add 24 to both sides and you'll get the number that goes in the blank (y)
10 = y

I'm not sure if this was helpful or confusing. I hope this makes sense. I'm not the best at explaining things, even if I understand them.

Answer 3

x = 2, y = -3
2x^2 + 3xy
substituting
2*2^2 + 3*2*(-3) = 8 - 18 = -10

and

x/3 + 1 = x-4
get all x on one side and all numbers on the other
5 = 2x/3
multiply both sides by 3/2
15/2 = x

and

2x + 3 = 3x + ____ x=-8
2x + 3 = 3x + y (find y when x = -8)
substitute for x
2*(-8) +3 = 3*(-8) + y
-16 + 3 = -24 + y
11 = y (so 11 goes in the blank)