How do I solve these inequalities questions?

Question

http://flickr.com/photos/16469112@N07/2129923715/

Question 6a b and c.
With workings and explanation.
Thank you very much.

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Answer 1

6a)
3x - 2½ ≥ 5x - 7¾
12x - 10 ≥ 20x - 29
19 ≥ 8x
x ≤ 19/8

6b)
18x + 24 > 20x - 10
34 < 2x
x > 17

6c)
3x + 3 - 1 ≤ 4x
2 ≤ x
x ≥ 2

Answer 2

Ok. You must be in Middle School I remember these problems. Its a good thing that I am a genius. Just check out the info on my profile.

For A
You have to simpify the ineqaulity to make it 8x. So you have a variable on only one side of the problem. (preferbly the left). Then add the fraction on the left to the fraction on the right. you should have 8x > (a fraction) then divide 8 by the fraction. And that should be your Answer.

B) You have to use the distributive property on both sides of the equation. So after you distribute it should look like this
18x + 24 >20x-10. Then you have to subtract (simpify) 18x and 20x to get the variable on one side. Which would equal 24 > 2x-10 the add 10 to 24 and you have 34>2x which you would divide 2 by 34. And the answer is X = 17

C) Same concept as A and B. But combined.

Answer 3

6a. 3x -- 2 1/2 ≥ 5x -- 7 3/4
=> 7 3/4 -- 2 1/2 ≥ 5x -- 3x
=> (7--2) (3/4--1/2) ≥ 2x
=> 5 1/4 ≥ 2x
=> x ≤ 1/2(5 1/4)
=> x ≤ 2 5/8 answer.
6b. 6(3x + 4) > 10(2x -- 3)
=> 9x + 12 > 10x -- 15
=> 27 > x
=> x < 27 answer.
6c. (x+1)/4 -- 1/12 ≤ x/3
=> 1/4 -- 1/12 ≤ x/3 -- x/4
=> 2/12 ≤ x/12
=> 2 ≤ x
Or x ≥ 2 answer.

Answer 4

I`m too lazy to solve it for you right now but working with inequalities is very similar to working with equal sign equations except that when you divide or multiply the equation by a negative number, the inequality sign is flipped. For the other operations (subtraction and addition) you can simply do it in the same way you do equal equations.

Answer 5

3x-2 1/2>=5x-7 4/3

by taking LCM we get..
(6x-5)/2 >=(20x-31)/4
by cross multipying...
24x-20>=40x-62
24x-40x>= -62+20
-16x >= -42
x >= -42/-16
therefore... x>=3

b. 6(3x+4)>10(2x-1)

by multiplying...
18x+24>20x-10
24+10>20x-18x
34>2x
34/2>x
therefore x<17

c.(x+1)/4-1/12<=x/3

LCM=12
((x+1)/4)*12 <=x/3*12
by dividin we get...
3(x+1)<=4x
3x +3<=4x
3x-4x<_=-3
-1x<= -3
therefore x<=3

Answer 6

the picture's really hard to see