What is the solution set for the inequation represented by the following number line?

1. {x ∈ R : -3 < x ≤ 4}

2. {x ∈ R : -3 < x < 4}

3. {x ∈ R : -3 ≤ x < 4}

4. {x ∈ R : -3 ≤ x ≤ 4}

The solution set of the inequation x - 3 ≥ -5, x ∈ R is :

1. {x : x > -2, x ∈ R}

2. {x : x ≤ -2, x ∈ R}

3. {x : x ≥ -2, x ∈ R}

4. {-2, -1, 0, 1, 2}

The solution set for the inequation 2x + 4 ≤ 14, x ∈ W is :

1. {1, 2, 3, 4, 5}

2. {0, 1, 2, 3, 4, 5}

3. {1, 2, 3, 4}

4. {0, 1, 2, 3, 4}

Case Study I

Shivam's father is a building contractor. One day Shivam got his father’s measuring tape. He used it to find the dimensions of the kitchen garden in his home. He found that the length of the garden is one metre more than twice its breadth. He told his friend Akhil that the perimeter of the garden is more than or equal to 110 m and is less than or equal to 140 m.

Based on this information, answer the following questions:

1. If breadth of the garden is x m, then the algebraic representation of the given information is:

1. 140 ≤ 6x + 2 ≤ 110, x ∈ R

2. 110 ≤ 6x + 2 ≤ 140, x ∈ R

3. 110 ≤ 4x + 2 ≤ 140, x ∈ R

4. 110 ≤ 2x + 1 ≤ 140, x ∈ R

2. The solution set for the breadth of the garden is:

1. {x ∈ R : 18 ≤ x ≤ 23}

2. {x ∈ R : 16 ≤ x ≤ 24}

3. {x ∈ R : 18 ≤ x ≤ 24}

4. {x ∈ R : 20 ≤ x ≤ 28}

3. The greatest possible value of the breadth of the garden is:

1. 18 m

2. 20 m

3. 22 m

4. 23 m

4. What is the least possible length of the garden?

1. 34 m

2. 36 m

3. 37 m

4. none of these

5. What is the greatest possible length of the garden?

1. 47 m

2. 51 m

3. 46 m

4. none of these