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Linear Inequalities — Class 11 solved problems

9 problems from this chapter, each solved step by step.

  1. Solve the following inequation: (x - 2)/(x + 5) > 2.

    x (-12, -5)

  2. Let the points ((11)/(2), α) lie on or inside the triangle with sides x + y = 11, x + 2y = 16, and 2x + 3y = 29. Then the product of the smallest and the larges

    33

  3. Solve 30 x<200 when (i) x is a natural number, (ii) x is an integer.

    (i) x 1, 2, 3, 4, 5, 6 (ii) x, 4, 5, 6

  4. Solve (3 x-4)/(2) ≥ (x+1)/(4)-1. Show the graph of the solutions on number line.

    The solution to the inequality is x ≥ 1.

  5. In an experiment, a solution of hydrochloric acid is to be kept between 30^(°) and 35^(°) Celsius. What is the range of temperature in degree Fahrenheit if conv

    The range of temperature in degree Fahrenheit is between 86^(°)F and 95^(°)F.

  6. Solve -5 ≤ (5-3 x)/(2) ≤ 8.

    -(11)/(3) ≤ x ≤ 5

  7. Solve the system of inequalities: & 3 x-7<5+x & 11-5 x ≤ 1 and represent the solutions on the number line.

    The solution to the system of inequalities is 2 ≤ x < 6.

  8. The marks obtained by a student of Class XI in first and second terminal examination are 62 and 48, respectively. Find the minimum marks he should get in the an

    The student must obtain a minimum of 70 marks in the annual examination.

  9. A manufacturer has 600 litres of a 12 % solution of acid. How many litres of a 30 % acid solution must be added to it so that acid content in the resulting mixt

    The manufacturer must add more than 120 litres but less than 300 litres of the 30% acid solution.

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