29) 4k - 1 >= -3

30) 6(c - 1) < -18
31) 3t > 5t + 12
32) -6/7y - 6 >= 42
33) 4 + x/2 > 2x
34) 3x + 5 <= 2x -8
35) 13.5a + 7.4 <= 85.7
36) 42w > 2(w +7)

ANSWERS:
29) k >= -2
30) c < -12
31) t < -6
32) y <= -56
33) x < 8/3
34) x <= -13
35) a <= 5.8
36) w > 7/20

have to get this in by tonight. if the problem looks wrong, tell me and i'll see if i missed anything. please help asap!

29.

4k-1 ≥ -3
4k ≥ -2
k ≥ -1/2

30.
6(c-1) ≤ -18
6c - 6 ≤ -18
6c ≤ -12
c ≤ -2

31.
3t > 5t + 12
-2t > 12
t < -6 , yeahhh you got it right

32.
-6/7y - 6 ≥ 42
multiply be 7
-6y - 42 ≥ 294
-6y ≥ 336
y ≤ -56 , yeahhh

33. correct
34. correct
35. correct
36. correct

After missing the first two, I was beginning to worry about you, but you finished strong at the end

29) its -1/2

30) (i forgot to continue :p) -2
im having trouble with 32. 30.86 or 41.86?

ill post more later. any help would be much appreciated.

nevermind!:) so they're all correct?

To solve these inequalities, we'll go through each question step by step. Here's how we can find the solutions to each inequality:

29) 4k - 1 >= -3

To isolate the variable k, we first add 1 to both sides:
4k - 1 + 1 >= -3 + 1
4k >= -2

Then, divide both sides by 4:
(4k)/4 >= (-2)/4
k >= -2/4
k >= -1/2

So the solution is k >= -1/2.

30) 6(c - 1) < -18

Start by distributing the 6:
6c - 6 < -18

Next, add 6 to both sides:
6c - 6 + 6 < -18 + 6
6c < -12

Divide both sides by 6:
(6c)/6 < (-12)/6
c < -2

The solution is c < -2.

31) 3t > 5t + 12

Start by subtracting 5t from both sides:
3t - 5t > 5t + 12 - 5t
-2t > 12

Divide both sides by -2, but remember to flip the inequality sign since we're dividing by a negative number:
(-2t)/-2 < 12/(-2)
t < -6

The solution is t < -6.

32) -6/7y - 6 >= 42

Start by adding 6 to both sides:
-6/7y - 6 + 6 >= 42 + 6
-6/7y >= 48

Next, multiply both sides by -7/6, again flipping the inequality sign:
(-6/7y)*(-7/6) <= 48*(-7/6)
y <= -56

The solution is y <= -56.

33) 4 + x/2 > 2x

Start by subtracting 2x from both sides:
4 + x/2 - 2x > 2x - 2x
4 - 2x + x/2 > 0

Let's get a common denominator for the second term:
4 - 4x/2 + x/2 > 0

Simplify:
4 - 2x + x/2 > 0

Combine like terms by finding a common denominator:
4*2/2 - 2x + x/2 > 0

8/2 - 2x + x/2 > 0

Simplify further:
4 - 2x + x/2 > 0

Multiply the whole equation by 2 to clear the fraction:
2(4 - 2x + x/2) > 0

Distribute the 2:
8 - 4x + x > 0

Combine like terms:
8 - 3x > 0

Subtract 8 from both sides:
8 - 8 - 3x > 0 - 8
-3x > -8

Divide both sides by -3, but remember to flip the inequality sign:
(-3x)/(-3) < (-8)/(-3)
x < 8/3

The solution is x < 8/3.

34) 3x + 5 <= 2x - 8

Start by subtracting 2x from both sides:
3x + 5 - 2x <= 2x - 8 - 2x
x + 5 <= -8

Then, subtract 5 from both sides:
x + 5 - 5 <= -8 - 5
x <= -13

The solution is x <= -13.

35) 13.5a + 7.4 <= 85.7

Start by subtracting 7.4 from both sides:
13.5a + 7.4 - 7.4 <= 85.7 - 7.4
13.5a <= 78.3

Then, divide both sides by 13.5:
(13.5a)/13.5 <= 78.3/13.5
a <= 5.8

The solution is a <= 5.8.

36) 42w > 2(w + 7)

Start by distributing the 2:
42w > 2w + 14

Next, subtract 2w from both sides:
42w - 2w > 2w + 14 - 2w
40w > 14

Then, divide both sides by 40:
(40w)/40 > 14/40
w > 7/20

The solution is w > 7/20.

I hope this helps! If you have any further questions, please let me know.