 |  Linear Inequalities 24 Flashcards |  Start |
 | Solve the inequality: 2x + 3y ≤ 12. What are the possible values of y when x = 0? |  Card: 1 / 24 |
| When x = 0, the inequality becomes 3y ≤ 12, which simplifies to y ≤ 4. Therefore, possible values of y are any number less than or equal to 4. | Card: 2 / 24 |
| True or False: The solution set for the inequality x + y > 5 includes the point (2, 3). | Card: 3 / 24 |
| True, because 2 + 3 = 5 does not satisfy the strict inequality, but points greater than (2, 3) do. | Card: 4 / 24 |
| Fill in the blank: For the inequality 4x - y ≤ 8, if x = 2, then y must be ___ or greater. | Card: 5 / 24 |
| Y must be 0 or greater, since 4(2) - y ≤ 8 simplifies to y ≥ 0. | Card: 6 / 24 |
| What is the graphical representation of the inequality y ≤ 2x + 3? | Card: 7 / 24 |
| The graph includes the line y = 2x + 3 and the area below this line, representing all points where y is less than or equal to 2x + 3. | Card: 8 / 24 |
| If the constraints are 2x + y ≤ 10 and x + 2y ≤ 8, determine the feasible region. | Card: 9 / 24 |
| The feasible region is the area on the graph where both inequalities are satisfied, typically shaded in the diagram. | Card: 10 / 24 |
| Fill in the blank: The inequality 3x + 4y > 12 represents a region above the line defined by ___ when rewritten as an equation. | Card: 11 / 24 |
| 3x + 4y = 12. | Card: 12 / 24 |
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| Given the inequalities x + y ≤ 6 and x - y ≥ 2, find the intersection point. | Card: 13 / 24 |
| To find the intersection point, solve the system: x + y = 6 and x - y = 2. The solution is (4, 2). | Card: 14 / 24 |
| What does the term 'bounded' mean in the context of a feasible region? | Card: 15 / 24 |
| A bounded feasible region is one that can be enclosed within a sufficiently large circle, meaning it does not extend to infinity. | Card: 16 / 24 |
| Fill in the blank: The solution set of the inequality 5x + 3y ≤ 15 is represented graphically as the area ___ the line 5x + 3y = 15. | Card: 17 / 24 |
| Below. | Card: 18 / 24 |
| True or False: Increasing the coefficients in an objective function will always lead to a higher maximum value. | Card: 19 / 24 |
| True, as increasing coefficients typically means a greater output for each unit of the variables. | Card: 20 / 24 |
| If you have the inequality 6x + 2y < 18, what is the maximum possible value of y when x / > | Card: 21 / 24 |
| Substituting x = 3 gives 6(3) + 2y < 18, which simplifies to 2y >< 0, so the maximum possible value of y is less than > | Card: 22 / 24 |
| What is the significance of extreme points in a feasible region? | Card: 23 / 24 |
| Extreme points are where the objective function achieves its maximum or minimum values, serving as crucial points for optimization. | Card: 24 / 24 |
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