Can you please look over these and let me know if they are right?

1/4(5x-1/2)-5/3<1/3 I got {x|x<51/30}

31-(2x+2)< or equal to 4(x+1)+x I got {x|x>equal to 3.6}

Use elimination method: 4x+5y=-12 and 7x-5y=-76 I got x=-8 and y=4

elimination: 0.3x-0.2y=4 and 0.4x+0.5y=1 I got the solution of (220/23,-130/23)

"1/4(5x-1/2)-5/3<1/3 I got {x|x<51/30} "

51/30 needs to be simplified, otherwise correct.

"31-(2x+2)< or equal to 4(x+1)+x I got {x|x>equal to 3.6} "
3.6 is almost right, I get 3 4/7.
Since the answer can be expressed in a fraction, there is no reason to use decimal approximation.

"Use elimination method: 4x+5y=-12 and 7x-5y=-76 I got x=-8 and y=4 "
correct!
"0.3x-0.2y=4 and 0.4x+0.5y=1 I got the solution of (220/23,-130/23) "
correct!

Let's go through each of the problems to check if the answers are correct.

For the first problem:
1/4(5x - 1/2) - 5/3 < 1/3
To solve this inequality, we start by distributing the 1/4 to the terms inside the parentheses:
(5/4)x - 1/8 - 5/3 < 1/3
Combining like terms:
(5/4)x - 1/8 - 40/8 < 8/24
(5/4)x - 41/8 < 1/3
Next, we can multiply both sides by 24 to eliminate fractions:
24[(5/4)x - 41/8] < 24(1/3)
6(5x - 41) < 8
30x - 246 < 8
30x < 254
x < 254/30
Simplifying the fraction:
x < 127/15
So the correct answer is {x | x < 127/15}, not {x | x < 51/30}.

For the second problem:
31 - (2x + 2) ≤ 4(x + 1) + x
To solve this inequality, we start by simplifying both sides:
31 - 2x - 2 ≤ 4x + 4 + x
Combining like terms:
29 - 2x ≤ 5x + 4
Next, we can subtract 5x from both sides:
29 - 7x ≤ 4
Subtracting 29 from both sides:
-7x ≤ -25
Dividing both sides by -7 (remember to flip the inequality sign when dividing by a negative number):
x ≥ -25/-7
Simplifying the fraction:
x ≥ 25/7
So the correct answer is {x | x ≥ 25/7}, not {x | x ≥ 3.6}.

Now let's move on to the third problem, which involves the elimination method for systems of equations:
4x + 5y = -12 (Equation 1)
7x - 5y = -76 (Equation 2)
To eliminate the variable "y," we can add Equation 1 to Equation 2:
(4x + 5y) + (7x - 5y) = (-12) + (-76)
Combining like terms:
11x = -88
Dividing both sides by 11:
x = -88/11
Simplifying the fraction:
x = -8
To find the value of "y," we can substitute the value of x into either Equation 1 or Equation 2. Let's use Equation 1:
4(-8) + 5y = -12
-32 + 5y = -12
Adding 32 to both sides:
5y = 20
Dividing both sides by 5:
y = 4
Therefore, the correct solution is x = -8 and y = 4.

Lastly, let's solve the system of equations using the elimination method:
0.3x - 0.2y = 4 (Equation 1)
0.4x + 0.5y = 1 (Equation 2)
To eliminate decimals, we can multiply Equation 1 by 10 and Equation 2 by 20 to get rid of the decimal points:
10(0.3x - 0.2y) = 10(4)
20(0.4x + 0.5y) = 20(1)
Simplifying:
3x - 2y = 40 (Equation 1)
8x + 10y = 20 (Equation 2)
Now, we can multiply Equation 1 by 5 and Equation 2 by 2 to get the same coefficient for "y":
5(3x - 2y) = 5(40)
2(8x + 10y) = 2(20)
Simplifying:
15x - 10y = 200 (Equation 1)
16x + 20y = 40 (Equation 2)
By adding Equation 1 to Equation 2, we can eliminate the variable "y":
(15x - 10y) + (16x + 20y) = 200 + 40
Combining like terms:
31x = 240
Dividing both sides by 31:
x = 240/31
So the x-coordinate is 240/31. To find the y-coordinate, we substitute this value into Equation 1:
3(240/31) - 2y = 40
720/31 - 2y = 40
Subtracting 720/31 from both sides:
-2y = 40 - 720/31
-2y = (40*31 - 720)/31
-2y = (1240 - 720)/31
-2y = 520/31
Dividing both sides by -2:
y = (520/31) / -2
y = 520/31 * -1/2
Simplifying:
y = -260/31
Therefore, the correct solution is (x, y) = (240/31, -260/31), not (220/23, -130/23).

I hope this helps clarify the correct answers for each problem.