Algebra II Honors—Day 6

Goals for Today Check Homework – Show me your homework to get a homework stamp – Go over questions from homework Essential Questions – New material Classwork practice on new material Review for Test

Warmup problems—work in your notes 1. Solve for h: 2.Solve. Graph solution on a number line and write the answer in both set notation and in interval notation.

Homework Questions?

Essential Questions How do I solve a compound inequality?

Notes Compound inequalities are inequalities that are joined by the word and or the word or. Solutions consist of the intersection (and) or the union (or) of the separate inequalities.

Examples Example 1 from the handout: This equation has two separate parts that must be solved separately. It is an INTERSECTION since the variable is in the expression in the middle. Split it up and solve each part. (See handout.) and Each part must be solved separately and the solutions combined—both must be true at the same time.

and Both of these inequalities are true when x is between -4 and 7. Solution: Set Notation: Interval Notation:

Example 2 from handout This one is a UNION—It’s true when EITHER of the two separate inequalities is true. Solution: OR Set notation: Interval notation:

Solving Absolute Value Inequalities

Absolute Value Inequalities are written as two compound inequalities and solved as INTERSECTIONS or as UNIONS. If and, then (intersection) If and, then OR (union) THESE RULES ALSO APPLY FOR ≤ AND ≥.

If the absolute value is less than a number or expression The inequality is an INTERSECTION (and). BOTH parts must be true at the same time. The variable will fall BETWEEN two values if there is a solution. (See example 2 on the back of the handout.) greater than a number or expression The inequality is a UNION (or). Either part may be true for inequality to be true. The solution will consist of all the possibilities for EITHER inequality. (See example 1 on the back of the handout.)

Classwork Practice Handout – 1-6 Study Guide and Intervention p. 31--#1, 3, 6, 8 p. 32--#2, 6, 8, 9

Homework Study for Test – Sets of numbers Venn diagram and relationships—Draw diagram and/or place numbers in correct spot Real, Irrational, Rational, Integer, Whole, Natural R, I, Q, Z, W, N Identify sets to which numbers belong – Linear Equations Standard Form, Slope-Intercept Form, finding intercepts, graphing, converting from one form to another – Accuracy of answers and units – Solve literal equations – Solving inequalities and compound inequalities – Solutions as set notation and as interval notation