explain algebra?

Question

(x=3)/8=x/2

(-2/3)x>12

5x<-7x-36

sorry i meant (x+3)/8=x/2

Answer 1

(x=3)/8=x/2

If you meant :
(x - 3)/8 = x/2, then
2(x - 3) = 8x
2x - 6 = 8x
- 6 = 8x - 2x = 6x
6x = - 6
x = - 1

(-2/3)x>12
(2/3)x < -12 !!!change of direction
x < -12(3/2)
x < - 18

5x<-7x-36
5x < - 7x - 36
5x + 7x < - 36
12x < - 36
x < - 3

Answer 2

in all of these problems you need to solve for x whcih means getting x alone on one side with the rest on the other side. A really important rule is to rmember that whatever you do to oneside of an equation you have to do to the other. treat the lessthan/greaterthan sign as an equal sign until you finish the problem. The only thinkg that would change it is if you divide by a negative munber andf then it switches the way the sign is facing

so the first one.... (x+3)/8=x/2

multiply both sides by 2
2 (x+3)/8=x
distribute the 2
2x+6/16=x
multiply both sides by 16
2x+6=16x
subrtract 2x from both sides
6=14x
divide both sides by 14
6/14=x

the 2nd one
(-2/3)x=12
think of -2/3 x as -2x/3
multiply both sides by 3
-2x=36
divide by -2 REMEBER THIS FLIPS THE SIGN
x=-18 so x<-18

5x=-7x-36
add 7x to both sides
12x=-36
divide both sides by 12
x=-3
x<-3

Answer 3

The first makes no sense to me.
The second: 2/3 x > -12; x > 3/2(12); x > 18.
Last: 5x < -7x - 36; 12x < -36; x < -3

Answer 4

If you meant (x+3) / 8 = x / 2, cross multiply.
2(x + 3) = 8x
2x + 6 = 8x

add -2x to both sides: 6 = 6x
Divide both by 6 to get x

On the next, multiply both sides by (-3/2) since that makes it just x. Switch the inequality from > to < because you multiplied by a negative.

The third, first add 7x to both sides to get 12x < -36. Then divide both sides by 12.

Answer 5

(x=3)/8=x/2 I think you mean (x+3)/8 =x/2.
This is a proportion so use cross multiplication getting:
8x = 2(x+3)
8x = 2x+6
6x=6
x=1

(-2/3)x>12
Multiply by -3/2 getting x < -18

5x<-7x-36
12x < -36
x < -3