Inequalities??

Question

solve each problem by writing an inequality

The length of a picture frame is 3 in. greater than the width. The perimeter is less than 52 in. Describe the dimensions of the frame.


Find the lesser of 2 consecutive intergers with a sum greater than 16.

Answer 1

Find the lesser of 2 consecutive intergers with a sum greater than 16.

(n) + (n+1) >16
2(n) +1 > 16
2(n) > 16-1
2(n) >15
n > (15/2)
n>7.5

n = 8 and n+1 = 9

check: 8+9 = 17 which is greater than 16


The length of a picture frame is 3 in. greater than the width. The perimeter is less than 52 in. Describe the dimensions of the frame.

l = length w = width
l =w+3

2(l+w) < 52
2(w+3+w) < 52
4w +6 < 52
4w < 46
2w < 23
w < 11.5 l = 14.5


w = 11 and l = 14 perimeter = 50 (which is less than 52).

Answer 2

#1)
2L+2W<52
2(3+W)+2W<52
6+2W+2W<52
6+4W<52
6-6+4W<52-6
4W<36
4W/4<36/4
W=9

L=3+W
L=3+9
L=11

Length is 11in and width is 9 in. to check u find the perimeter and the perimeter must be less than 52 in

P<52
2L+2W<52
2*11+2*9<52
22+18<52
40<52 and this statement is correct because 40 is less than 52.


#2)
x+x+1>16
2x+1>16
2x+1-1>16-1
2x>15
2x/2>15/2
x>7.5

7.5+1=8.5

The two consectutive numbers are 7.5 and 8.5.

Answer 3

l = w + 3
P < 52

52 > 2(w + l)

52 > 2(w + (w + 3))
52 > 2(w + w + 3)
52 > 2(2w + 3)
26 > 2w + 3
23 > 2w
w < 11.5 inches

l = 11.5 + 3
l = 14.5

At most the dimensions are

Length = 14 inches
Width = 11 inches

------------------------------------

x + (x + 1) > 16
x + x + 1 > 16
2x + 1 > 16
2x > 15
x > 7.5

ANS : 8

Answer 4

l = 3 + w
2l+2w<52
2(3+w)+2w<52
6+4w<52
w<23/2
l < 29/2

b = a +1
a + b > 16
2a+1>16
a>15/2 or a>=8
b>17/2 or b>=9