Linear Inequalities quiz

The solution of 2x > 8 for real x is:

If -3x > 9, then:

The natural number solutions of x + 2 < 5 are:

On the number line, x > 2 is shown by:

The solution of -1 < x + 1 < 3 is:

Which of these is a slack inequality?

If x is an integer and -2 <= x < 2, the number of values of x is:

The solution of 5 - 2x <= 1 is:

If 3x - 7 > 5x - 1, then:

The solution of x/3 > x/2 + 1 is:

Solve 5x - 3 < 3x + 1 for real x. (2 marks)

Solve 3(2 - x) >= 2(1 - x). (2 marks)

Solve x/2 >= (5x - 2)/3 - (7x - 3)/5. (2 marks)

Solve 2(2x + 3) - 10 < 6(x - 2). (2 marks)

Solve -12 < 4 - 3x <= 2 for real x. (2 marks)

Solve 3 - 2x >= 4x - 9 and represent on the number line. (2 marks)

Find all pairs of consecutive even positive integers both larger than 5 whose sum is less than 23. (2 marks)

Solve 37 - (3x + 5) >= 9x - 8(x - 3). (2 marks)

Solve (x - 2)/4 + 1 > (x + 4)/3. (2 marks)

Solve 2 <= 3x - 4 <= 5. (2 marks)

The marks of a student in four tests are 62, 48, 65 and 70. What is the minimum score she must get in the fifth test to have an average of at least 60? (3 marks)

The temperature in Fahrenheit is given by F = (9/5)C + 32. If a solution must be kept between 68 and 77 degrees F, find the range in degrees C. (3 marks)

The cost of making x items is C = 26,000 + 30x and the revenue is R = 43x. How many items must be sold to make a profit? (3 marks)

The longest side of a triangle is 3 times the shortest side, and the third side is 2 cm shorter than the longest side. If the perimeter is at least 61 cm, find the minimum length of the shortest side. (3 marks)

A man wants to cut three lengths from a 300 cm board. The second is 5 cm longer than the first and the third is twice the first. If the total must not exceed 300 cm, find the maximum length of the first piece. (3 marks)

Read the passage and answer the questions. A mobile company offers a plan of Rs 300 a month plus Rs 1.50 per minute of calls. Another company offers Rs 450 a month with unlimited calls. (i) Write the monthly cost of the first plan for x minutes. (ii) Write an inequality for when the first plan is cheaper. (iii) Solve it. (5 marks)

Read the passage and answer the questions. A shopkeeper buys pens at Rs 15 each and sells them at Rs 22 each. His fixed costs are Rs 700 per month. (i) Write the profit for x pens. (ii) Write an inequality for a profit of at least Rs 1,400. (iii) Find the minimum number of pens he must sell. (5 marks)

Read the passage and answer the questions. A student scored 72, 65 and 80 in three tests. To get grade A, his average in four tests must be at least 75. (i) Write the inequality. (ii) Solve it. (iii) If the maximum mark is 100, can he get grade A? (5 marks)

Read the passage and answer the questions. A medicine must be stored between 2 and 8 degrees Celsius. A cold storage records temperatures in Fahrenheit. (i) Write the inequality in C. (ii) Convert it to F using F = (9/5)C + 32. (iii) Is 50 degrees F safe? (5 marks)

Read the passage and answer the questions. A lift can carry at most 680 kg. A man weighing 80 kg wants to load boxes of 60 kg each. (i) Write an inequality for the number of boxes x. (ii) Solve it. (iii) Find the maximum number of boxes. (5 marks)

Explain the rules for solving linear inequalities in one variable with examples. Why is the sign reversed when multiplying by a negative number? (6 marks)

Solve (2x - 1)/3 >= (3x - 2)/4 - (2 - x)/5 and represent the solution on the number line. (6 marks)

Solve the system of inequalities 2x + 1 > 3 and 3x - 2 <= 10, and represent the solution set on the number line. (6 marks)

In an experiment, a solution of hydrochloric acid is to be kept between 30 and 35 degrees Celsius. What is the range of temperature in degrees Fahrenheit? (6 marks)

How many litres of water must be added to 1,125 litres of a 45% acid solution so that the resulting mixture contains more than 25% but less than 30% acid? (6 marks)