Answer:
1.) Let x be the number. The inequality can be written as:
x + 7 < 18
Subtracting 7 from both sides, we get:
x < 11
Therefore, the number is less than 11.
2.) Let x be the number. The inequality can be written as:
x + 5 > 26
Subtracting 5 from both sides, we get:
x > 21
Therefore, the number is greater than 21.
3.) Let x be the first integer. The second integer is x+1. The inequality can be written as:
x + (x+1) < 55
Simplifying, we get:
2x + 1 < 55
Subtracting 1 from both sides, we get:
2x < 54
Dividing both sides by 2, we get:
x < 27
Therefore, the largest possible first integer is 26, and the second integer is 27. Their sum is 53.
4.) Let w be the width of the rectangle. The length is 4cm longer than the width, so the length is w + 4. The perimeter is given by:
2(length + width) ≤ 28
Substituting the expressions for length and width, we get:
2(w + 4 + w) ≤ 28
Simplifying, we get:
4w + 8 ≤ 28
Subtracting 8 from both sides, we get:
4w ≤ 20
Dividing both sides by 4, we get:
w ≤ 5
Therefore, the maximum possible width is 5cm, and the maximum possible length is 9cm.
5.) Let x be the first odd integer. The second and third odd integers are x+2 and x+4, respectively. The inequality can be written as:
x + (x+2) + (x+4) ≥ 51
Simplifying, we get:
3x + 6 ≥ 51
Subtracting 6 from both sides, we get:
3x ≥ 45
Dividing both sides by 3, we get:
x ≥ 15
Therefore, the smallest possible first odd integer is 15, and the second and third odd integers are 17 and 19, respectively. The middle integer is 17.
Explanation: