Today is our topic of discussion Inequality exercises – 6.2 .
Inequality exercises – 6.2
1. Which one is the solution set of the inequality 5x + 5 > 25?
1) S = {x ∈ Rx > 4}
3) S = {x ∈ R: x < 4}
2) S = {x ∈ R: x < 4}
4) S = {x ∈ Rx ≥4}
2. For which value of x, it will be y = 0 for the equation x + y = -2?
1) 2
2) 0
3) 4
4) -2
3. Which are the correct co-oridnates of the equation 2xy + y = 3?
1) (1,-1), (2, -1)
2) (1,1), (-1,-3)
3) (1,1), (-2,1)
4) (-1, 1), (2, -1)
Answer the question 4 and 5 from the inequality given below:
4. Which one is the solution set of the inequality?
1) S = {x Rx > 4}
3) S = {xR: x ≤ 4}
2) S = {TER: x < 4}
4) S= {x Rx > 4}
5. Which one is the number line of the solution set of the above inequality ?
6. For the inequality 3x + 6 > 9
(i) Dividing both sides by 3, we get x + 2 > 3
(ii) Solution set = {x ∈ R x > 1}
(iii) Solution set in the number line:
Which of the followings is correct?
1) i and ii
2) i and iii
3) ii and iii
4) i, ii and iii
7. The ages of Rita, Mita and Bithi are x, 2x and 3x years respectively. If the sum of their age is not more than 60 years
(i) the mathematical expression of the problem is x + 2x + 3x ≤ 60
(ii) age of Rita is ≤ 10 years
(iii) age of Mita is > 20 years
Which of the followings is correct?
1) i, ii
2) i, iii
3) ii, iii
4) i, ii and iii
8. a, b and c are three real numbers. If a > b and c #0
(i) ac> bc when c> 0
(ii) ac< be when c <0
(iii) when c> 0 a C с
Which of the following is correct?
1) i, ii
2) i, iii
3) ii, iii
4) i, ii and iii
9. Draw the graph of the following inequalities:
1) x – y > -10
2) 2x – y < 6
3) 3x – y ≥0
4) 3x-2y≤ 12
5) y <-2
7) y > x+2
6) x ≥ 4
8) y < x+2
9) y ≥ 2x
10) x + 3y <0
10. The air distance of the Singapore airport from the Hazrat Shahjalal airport is 2900 km. The maximum speed of the Bangladesh Biman is 500 km/hour. But on the way from the Hazrat Shahjalal airport, it faces air flowing at 60 km/hour from the opposite direction.
1) Express the problem of stimulus in terms of an inequality taking the required time as t hours.
2) Find the required time of non-stop flying from the Hazrat Shahjalal airport to the Singapore airport using the inequality in 10(1) and show it on a number line.
3) Take x as time of returning from the Singapore airport to the Hazrat Shahjalal airport and then express the problem in the form of an inequality and solve it graphically.
11. Between two numbers, the result of subtraction of 5 times of the second number from 3 times of the first one is greater than 5. Again, when 3 times of the second number is subtracted from the first one, the result is not more than 9.
1) Express the conditions stated by stimulus in the form of inequalities.
2) If 5 times of the first number is less than the sum of twice the first number and 15, express the possible values of the number in the form of an inequality.
3) Draw the graph of each pair of inequalities obtained in 1).
12. The sum of price of a pen, an eraser and a notebook is Tk. 100. Price of a notebook is more than the price of two pens. Price of three pens is more than the price of four erasers and price of three erasers is more than that of a notebook. If the price of all the commodities are in integers, what are the prices of each commodity?
13. The product of three integers is 720. What can be the maximum value of the smallest number?
14. If an isosceles triangle is divided into two isosceles triangles using the bisector of an angle of that triangle, what can be the maximum value of an angle of the first isosceles triangle? What can be the minimum value of an angle of the first isosceles triangle?
15. 7 tables, all of which have an area of one square meter can be placed in a rectangular room. If the perimeter of the room is 16 meters, what can be the length and the width of the room?
16. Is there any triangle whose height from the vertex can not be more than 1 cm but the area is 100 square?
17. Satej and Sajib are twin brothers. Their velocity in both running and walking are same. One day on the way to school, Satej passed half of the road by walking, while passed the rest by running. But Sajib passed half of the time by walking, while passed the rest by running. Will it take the same time for them to go to school?
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