Linear Inequalities

Topics in this chapter

• One-Variable Inequality Solving
• Compound Inequalities and Intervals
• Two-Variable Inequality Graphs
• Systems and Feasible Regions
• Integer Solutions and Vertices
• Inequality Word Problems and Parameters

Cheat sheet

Practice questions

1. Question 1Q-99EE6B

   Solve the inequality 5 - 2x ≥ 11.

   1. A.x ≥ -3
   2. B.x ≤ -3
   3. C.x ≥ 3
   4. D.x ≤ 3
   See the answer and solution
2. Question 2Q-DE2249

   Find the solution set of the compound inequality -2 ≤ 3x + 1 < 10.

   1. A.-1 ≤ x < 3
   2. B.-1 < x ≤ 3
   3. C.-3 ≤ x < 9
   4. D.1 ≤ x < 3
   See the answer and solution
3. Question 3Q-D5566E

   The feasible region is defined by x + y ≤ 5, x - y ≥ 1, x ≥ 0, and y ≥ 0. Which set contains all its vertices?

   1. A.(1, 0), (5, 0), (3, 2)
   2. B.(0, 1), (0, 5), (2, 3)
   3. C.(1, 0), (5, 0), (2, 3)
   4. D.(0, 0), (5, 0), (3, 2)
   See the answer and solution
4. Question 4Q-17C4BA

   For a real parameter k, solve the inequality (k - 2)x ≤ 3, giving the solution set separately for k > 2, k = 2, and k < 2.

   See the answer and solution
5. Question 5Q-1D1F77

   Solve the inequality 4x − 7 ≤ 9.

   1. A.x < 4
   2. B.x ≤ 4
   3. C.x ≥ 4
   4. D.x > 4
   See the answer and solution