I need help solving these inequalities!!?

Question

1) If twice an integer increased by 12 lies between 20 and 24, what is the integer?

2) Find the coordinates of the midpoint of the line segment whose endpoints are (8,10) and (-2,7)

Answer 1

20 < 2x +12 <24

8< 2x < 12

4 < x < 6

Therefore x must equal 5.

Y2 - Y1  = 10-7 = 3

X2 - X1 = 8 +2 = 10

m = 3/10

y = (3/10)x +b

10 = 2.4 + b

b = 7.6

y = (3/10)x + 7.6

y = (3/10)(3) +7.6

y = 8.5

(3, 8.5)

Or you could have just added up the x and y componets and divided by 2.

Answer 2

(1) Let the integer be x. as given 20 < 2x + 12 < 24

8 < 2x < 12  OR 4 < x < 6 that means x = 5. The required integer is 10 + 12 = 22.

(2) Use mid point formula of coordinate geometry. Thus the mid point is

  {[8 + ( - 2)]/2 , [10 + 7]/2} = ( 3 , 17/2) This is the mid point

Answer 3

1)20<(x+12)*2<24

10<x+12<12

-2<x<0 => x=-1

2) (x1,y1)=(8,10)

    (x2,y2)=(-2,7)

(x,y)- mid point

x=(x1+x2)/2

y=(y1+y2)/2

x=(8-2)/2=6/2=3

y=(10+7)/2=17/2=8.5

Solution: (x,y)=(3,8.5)

--Anna

Answer 4

1) 20<x*2 + 12<24

8<x*2<12

4<x<6

answer must be 5

2) (8-2)/2,(10+7)/2           (just average both components)

=(3,17/2)

Answer 5

1) 5

2) (3,8.5)