Test #5
5-1
1. Inequality- An open sentence that contains the symbol <, ≤, >, or ≥.
2. Addition Property of Inequalities- If the same number is added to each side of a true inequality, the resulting inequality is also true.
3. Set-Builder Notation- A concise way of writing a solution set. For example, {t|t<17} represents the set of all numbers t such that t is less than 17.
4. Subtraction Property of Inequalities- If the same number is subtracted from each side of a true inequality, the resulting inequality is also true.
5-2
5. Multiplication Property of Inequalities- If both sides of an inequality that is true are multiplied by a positive number, the resulting inequality is also true. If both sides of an inequality that is true are multiplied by a negative number, the direction of the inequality sign is reversed to make the resulting inequality also true.
6. Division Property of Inequalities- If both sides of a true inequality are divided by a positive number, the resulting inequality is also true. If both sides of a true inequality are divided by a negative number, the direction of the inequality sign is reversed to make the resulting inequality also true.
5-3 None
5-4
7. Compound Inequality- Two or more inequalities that are connected by words and or or.
8. Intersection- The graph of a compound inequality containing and; the solution is the set of elements common to both inequalities.
9. Union- The graph of a compound inequality containing or; the solution is a solution of either inequality, not necessarily both.
5-5 None
5-6
10. Boundary- A line or curve that separates the coordinate plane into regions.
11. Half-Planes- The region of the graph of an inequality on one side of a boundary.
12. Closed Half-Plane- The solution of a linear inequality that includes the boundary line.
13. Open Half-Plane- The solution of a linear inequality that does not include the boundary line.
5-1
1. Inequality- An open sentence that contains the symbol <, ≤, >, or ≥.
2. Addition Property of Inequalities- If the same number is added to each side of a true inequality, the resulting inequality is also true.
3. Set-Builder Notation- A concise way of writing a solution set. For example, {t|t<17} represents the set of all numbers t such that t is less than 17.
4. Subtraction Property of Inequalities- If the same number is subtracted from each side of a true inequality, the resulting inequality is also true.
5-2
5. Multiplication Property of Inequalities- If both sides of an inequality that is true are multiplied by a positive number, the resulting inequality is also true. If both sides of an inequality that is true are multiplied by a negative number, the direction of the inequality sign is reversed to make the resulting inequality also true.
6. Division Property of Inequalities- If both sides of a true inequality are divided by a positive number, the resulting inequality is also true. If both sides of a true inequality are divided by a negative number, the direction of the inequality sign is reversed to make the resulting inequality also true.
5-3 None
5-4
7. Compound Inequality- Two or more inequalities that are connected by words and or or.
8. Intersection- The graph of a compound inequality containing and; the solution is the set of elements common to both inequalities.
9. Union- The graph of a compound inequality containing or; the solution is a solution of either inequality, not necessarily both.
5-5 None
5-6
10. Boundary- A line or curve that separates the coordinate plane into regions.
11. Half-Planes- The region of the graph of an inequality on one side of a boundary.
12. Closed Half-Plane- The solution of a linear inequality that includes the boundary line.
13. Open Half-Plane- The solution of a linear inequality that does not include the boundary line.