i have a couple questions
what are the least common multiples of these number sets (30,65) (66,55,44) (29,58,4)(20,55)(180,252) and 21,16
then i need someone to solve these inequalitys
x-7<-8 3t<15 3w>30 4n+8<24 6y+1<19
2r-8>6 b-5>-2 2y+1<-5 4x-6>-10
thanks in advance
I will do one for you:
(66,55,44)
66 = 11*3*2
55 = 11*5
44 = 11*2*2
So we will need 11*2*2*3*5 = 660
do the others the same way
I will do the last of the second batch
4x-6>-10
4x > -10 + 6
4x > -4
x > -1
There is only one thing you have to keep in mind.
If in the last step you either multiply or divide by a negative, the inequality sign has to be reversed.
e.g.
-3x > 15
x < -5
Sure, I can help you with that! Let's start with finding the least common multiples of the given number sets.
To find the least common multiple (LCM) of a set of numbers, we need to determine the smallest multiple that is divisible by all the numbers in the set. We can find the LCM by listing out the multiples of each number until we find a common multiple.
For the number set (30, 65), we can list out multiples:
30: 30, 60, 90, 120, ...
65: 65, 130, 195, 260, ...
The least common multiple is the smallest number that appears in both lists, which in this case is 195. So, the LCM of 30 and 65 is 195.
Now, let's move on to the next number set (66, 55, 44):
66: 66, 132, 198, 264, ...
55: 55, 110, 165, 220, ...
44: 44, 88, 132, 176, ...
The least common multiple among these numbers is 132. So, the LCM of 66, 55, and 44 is 132.
Next, for the number set (29, 58, 4):
29: 29, 58, 87, 116, ...
58: 58, 116, 174, 232, ...
4: 4, 8, 12, 16, ...
The least common multiple here is 116. So, the LCM of 29, 58, and 4 is 116.
For the number set (20, 55):
20: 20, 40, 60, 80, ...
55: 55, 110, 165, 220, ...
The least common multiple is 220. So, the LCM of 20 and 55 is 220.
Moving on to the number set (180, 252):
180: 180, 360, 540, 720, ...
252: 252, 504, 756, 1008, ...
The least common multiple is 504. So, the LCM of 180 and 252 is 504.
Lastly, for the number set (21, 16):
21: 21, 42, 63, 84, ...
16: 16, 32, 48, 64, ...
The least common multiple is 336. So, the LCM of 21 and 16 is 336.
Now, let's move on to solving the inequalities you provided:
1) x - 7 < -8
To solve this inequality, we will isolate the variable x:
x - 7 + 7 < -8 + 7
x < -1
2) 3t < 15
To solve for t, divide both sides of the inequality by 3:
(3t)/3 < 15/3
t < 5
3) 3w > 30
To solve for w, divide both sides of the inequality by 3, but remember to flip the inequality sign since we are dividing by a negative number:
(3w)/3 > 30/3
w > 10
4) 4n + 8 < 24
To solve for n, isolate the variable by subtracting 8 from both sides:
4n + 8 - 8 < 24 - 8
4n < 16
n < 4
5) 6y + 1 < 19
To solve for y, isolate the variable by subtracting 1 from both sides:
6y + 1 - 1 < 19 - 1
6y < 18
y < 3
6) 2r - 8 > 6
To solve for r, isolate the variable by adding 8 to both sides:
2r - 8 + 8 > 6 + 8
2r > 14
r > 7
7) b - 5 > -2
To solve for b, isolate the variable by adding 5 to both sides:
b - 5 + 5 > -2 + 5
b > 3
8) 2y + 1 < -5
To solve for y, isolate the variable by subtracting 1 from both sides:
2y + 1 - 1 < -5 - 1
2y < -6
y < -3
9) 4x - 6 > -10
To solve for x, isolate the variable by adding 6 to both sides:
4x - 6 + 6 > -10 + 6
4x > -4
x > -1
I hope this helps! Let me know if you have any further questions.