Transcript inequality
ALGEBRA CHAPTER 3 Solving and Graphing Linear Inequalities ONE-STEP LINEAR INEQUALITIES—3.1 VOCABULARY An equation is formed when an equal sign (=) is placed between two expressions creating a left and a right side of the equation An equation that contains one or more variables is called an open sentence When a variable in a single-variable equation is replaced by a number the resulting statement can be true or false If the statement is true, the number is a solution of an equation Substituting a number for a variable in an equation to see whether the resulting statement is true or false is called checking a possible solution INEQUALITIES Another type of open sentence is called an inequality. An inequality is formed when and inequality sign is placed between two expressions A solution to an inequality are numbers that produce a true statement when substituted for the variable in the inequality INEQUALITY SYMBOLS Listed below are the 4 inequality symbols and their meaning < Less than ≤ Less than or equal to > Greater than ≥ Greater than or equal to Note: We will be working with inequalities throughout this course…and you are expected to know the difference between equalities and inequalities GRAPHS OF LINEAR INEQUALITIES Graph (1 variable) The set of points on a number line that represents all solutions of the inequality GRAPHS OF LINEAR INEQUALITIES GRAPHS OF LINEAR INEQUALITIES WRITING LINEAR INEQUALITIES Bob hopes that his next math test grade will be higher than his current average. His first three test scores were 77, 83, and 86. Why would an inequality be best in this case? How can we come up with this inequality? Graph! SOLVING ONE-STEP LINEAR INEQUALITIES Equivalent Inequalities Two or more inequalities with exactly the same solution Manipulating Inequalities All of the same rules apply to inequalities as equations* When multiplying or dividing by a negative number, we have to switch the inequality! Less than becomes greater than, etc. SOLVING WITH ADDITION/SUBTRACTION SOLVING WITH ADDITION/SUBTRACTION SOLVING WITH MULTIPLICATION/DIVISION SOLVING WITH MULTIPLICATION/DIVISION WHY DO WE HAVE TO CHANGE THE SIGN? Is there another way we can solve this? ALGEBRA CHAPTER 3 Solving and Graphing Linear Inequalities SOLVING MULTI-STEP LINEAR INEQUALITIES—3.2 MULTI STEP INEQUALITIES Treat inequalities just like you would normal, everyday equations* *change the sign when multiplying or dividing by a negative!! EXAMPLES: EXAMPLES: EXAMPLES: EXAMPLES: EXAMPLE You plan to publish an online newsletter that reports the results of snow cross competitions. You do not want your monthly costs to exceed $2370. Your fixed monthly costs are $1200. You must also pay $130 per month to each article writer. How many writers can you afford to hire in a month? EXAMPLES: TRY THESE ON YOUR OWN! 1) WHICH GRAPH REPRESENTS THE CORRECT k ANSWER TO 4 1. 2. 3. 4. -5 -5 -5 -5 >1 o -4 o -4 ● -4 ● -4 Answer Now -3 -3 -3 -3 x 2) WHEN SOLVING > -10 3 WILL THE INEQUALITY SWITCH? 1. 2. 3. Yes! No! I still don’t know! Answer Now 3) WHEN SOLVING a 6 4 WILL THE INEQUALITY SWITCH? 1. 2. 3. Yes! No! I still don’t know! Answer Now 4) SOLVE -8P ≥ -96 1. 2. 3. 4. p ≥ 12 p ≥ -12 p ≤ 12 p ≤ -12 Answer Now 5) SOLVE 7V < -105 1. 2. 3. 4. o -16 -15 -14 o -16 -15 -14 ● -16 -15 ● -14 -15 -15 -14 Answer Now CLASS WORK: P.343 #15-37 ODD IF YOU DO NOT FINISH IN CLASS, THEN IT BECOMES HOMEWORK! ALGEBRA CHAPTER 3 Solving and Graphing Linear Inequalities COMPOUND INEQUALITIES—3.6 COMPOUND INEQUALITY What does compound mean? Compound fracture? So…what’s a compound inequality? An inequality consisting of two inequalities connected by an and or an or GRAPHING COMPOUND INEQUALITIES Graph the following: GRAPHING COMPOUND INEQUALITIES Graph the following: GRAPHING COMPOUND INEQUALITIES Graph the following: All real numbers that are greater than or equal to -2 and less than 3 SOLVING COMPOUND INEQUALITIES Again….treat these like equations! Whenever we do something to one side… …We do it to every side! SOLVING COMPOUND INEQUALITIES SOLVING COMPOUND INEQUALITIES SOLVING COMPOUND INEQUALITIES SOLVING COMPOUND INEQUALITIES HOMEWORK: P.349 #12-36 EVEN SOLVING ABSOLUTE-VALUE EQUATIONS AND INEQUALITIES—3.6 (DAY 1) ABS. VALUE What is Absolute Value? Distance from zero What does that mean? ABS. VALUE So….an absolute value equation has how many solutions? Is this always true? ABS. VALUE How do we apply this to equations? Ex: EXAMPLES EXAMPLES EXAMPLES EXAMPLES EXAMPLES P.356#19-36 SOLVING ABSOLUTE-VALUE EQUATIONS AND INEQUALITIES—3.6 (DAY 2) ABSOLUTE VALUE AND INEQUALITIES ABSOLUTE VALUE AND INEQUALITIES EXAMPLES EXAMPLES EXAMPLES