Reteach Solving Absolute-Value Equations and Inequalities

1 Copyright by Holt, Rinehart and Winston. 62 Holt Algebra 2 All rights Date ClassReteachSolving Absolute-Value Equations and Inequalities2-8 LESSONTo solve compound Inequalities , solve both Inequalities . Then x 6 4 or 2x 6 4 OR 2x 8x 2 OR x 4 Solve x 2 1 and 3x 2 1 AND 3x 12x 3 AND x 4 Solve and graph each compound inequality. 3 2 or 1 __ 2 x 1 2. 6x 18 and x 6 6x OR x x AND x 012345 012345 4 7 or 4x 4 4. 3x 6 and x 2 5 OR AND 012345 012345 5.

2 3x 12 and 3x 12 6. 1 __ 2 x 2 0 or 2 1 __ 2 x 1 This inequality uses OR. Its graph has two the inequality when dividing by a negative inequality uses AND. Its graph has one 012345 6212/7/05 6:27:14 PMCopyright by Holt, Rinehart and Winston. 63 Holt Algebra 2 All rights Absolute-Value Equations and Inequalities (continued)Name Date Class2-8 LESSON Solving Absolute-Value Inequalities is like Solving compound : x 2 Solution: 2 x 2 Solve: x 2 Solution: 2 x 2 Solve: x 2 Solution: x 2 OR x 2 Solve: x 2 Solution: x 2 OR x 2 Solve x 2 3.

3 3 x 2 3 3 2 x 2 2 3 2 Add 2. 1 x 5 Simplify. Solve 2x 1 5. 2x 1 5 OR 2x 1 5 2x 6 OR 2x 4 Add 1. x 3 OR x 2 Divide by 2. Solve and graph. 7. x 3 2 8. 2x 1 3 2 x 3 2 2x 1 3 OR 2x 1 3 5 x 1 2x 2 OR 2x 4 x 1 OR x 2 Remember: x x if x 0 Use the solutions from the table to write the 634/28/06 5:31:58 PM4/28/06 5:31:58 PMProcess BlackProcess BlackCopyright by Holt, Rinehart and Winston. 89 Holt Algebra 2 All rights reserved.#OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !))

4 LGEBRA !LL RIGHTS RESERVED ,%33/. n* >V Vi 3 OLVING !BSOLUTE 6 ALUE %QUATIONS AND )NEQUALITIES3 OLVE EACH COMPOUND INEQUALITY 4 HEN GRAPH THE SOLUTION X AND X X AND X X OR X X OR X X AND X X AND X 3 OLVE EACH EQUATION X X X X OR X X OR X X OR X X OR X $ETERMINE WHETHER EACH INEQUALITY IS A CONJUNCTION OR A DISJUNCTION AND WHETHER YOU WOULD USE AND OR OR X X X $ISJUNCTION OR #ONJUNCTION AND $ISJUNCTION OR3 OLVE EACH INEQUALITY 4 HEN GRAPH THE SOLUTION X ???????? X ?? X ?? X OR X 0 HIL TOLD HIS FRIEND THAT IF YOU SUBTRACT FROM HIS AGE AND THEN TAKE THE absolute value YOU LL GET AN ANSWER OF (OW OLD IS 0 HIL OR #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON }iL > !)

5 LL RIGHTS RESERVED --" n* >V Vi 3 OLVING !BSOLUTE 6 ALUE %QUATIONS AND )NEQUALITIES3 OLVE EACH EQUATION X X X { { X X X X x X n X 3 OLVE EACH INEQUALITY OR COMPOUND INEQUALITY 4 HEN GRAPH THE SOLUTION X AND X X OR X { { { X \ X \ x X X > ` 3 OLVE !NY MEASUREMENT IS ACCURATE WITHIN OF THE MEASUREMENT UNIT &OR EXAMPLE IF YOU MEASURE YOUR PENCIL TO THE NEAREST INCH YOUR MEASUREMENT COULD BE INCH TOO LONG OR INCH TOO SHORT 7 RITE AN absolute value INEQUALITY THAT SHOWS THE MAXIMUM AND MINIMUM ACTUAL MEASURE OF A NAIL MEASURED TO BE CENTIMETERS TO THE NEAREST CENTIMETER { { x#OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !)}}}}}}}

6 LGEBRA !LL RIGHTS RESERVED ,%33/.* >V Vi 3 OLVING !BSOLUTE 6 ALUE %QUATIONS AND )NEQUALITIES n3 OLVE EACH EQUATION X ?? X X X OR X X OR X X OR X 3 OLVE AND GRAPH S X D AND X X ??????? OR X X ??? X X X ?????? X X ?? OR X ?? X ?? OR X ?? X X ???????? X OR X X AND X ?? 3 OLVE "EN SAYS THAT THERE IS NO SOLUTION FOR THIS absolute value INEQUALITY )S HE CORRECT )F NOT SOLVE THE INEQUALITY %XPLAIN HOW YOU KNOW YOU ARE CORRECT X ??????? 0 OSSIBLE ANSWER "EN IS CORRECT 4 HERE IS NO SOLUTION 7 HEN THE INEQUALITY IS SIMPLIFIED THE RESULT IS AN INEQUALITY THAT SETS THE absolute value OF AN EXPRESSION LESS THAN A NEGATIVE NUMBER 3 INCE absolute VALUES ARE ALWAYS POSITIVE THIS IS NEVER TRUE #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON }iL > !

7 LL RIGHTS RESERVED ,i i>V 3 OLVING !BSOLUTE 6 ALUE %QUATIONS AND )NEQUALITIES n --" 4O SOLVE COMPOUND Inequalities SOLVE BOTH Inequalities 4 HEN GRAPH 3 OLVE X OR X X /2 X X /2 X 3 OLVE X AND X X !.$ X X !.$ X 3 OLVE AND GRAPH EACH COMPOUND INEQUALITY X OR ?? X X AND X X /2 X X !.$ X X OR X X AND X /2 !.$ X AND X ?? X OR ?? X { > ` { { 4 HIS INEQUALITY USES /2 )TS GRAPH HAS TWO PARTS 2 EVERSE THE INEQUALITY WHEN DIVIDING BY A NEGATIVE NUMBER 4 HIS INEQUALITY USES !.$ )TS GRAPH HAS ONE PART 896/9/06 12:37:21 PM6/9/06 12:37:21 PMCopyright by Holt, Rinehart and Winston.}}}

8 90 Holt Algebra 2 All rights reserved.#OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL RIGHTS RESERVED ,i i>V 3 OLVING !BSOLUTE 6 ALUE %QUATIONS AND )NEQUALITIES CONTINUED n,%33/. 3 OLVING absolute value Inequalities IS LIKE Solving COMPOUND Inequalities 3 OLVE X 3 OLUTION X 3 OLVE X 3 OLUTION X 3 OLVE X 3 OLUTION X /2 X 3 OLVE X 3 OLUTION X /2 X 3 OLVE X X X !DD X 3 IMPLIFY 3 OLVE X X /2 X X /2 X !DD X /2 X $IVIDE BY 3 OLVE AND GRAPH X X X X /2 X X X /2 X X /2 X 2 EMEMBER X X IF X 5SE THE SOLUTIONS FROM THE TABLE TO WRITE THE Inequalities #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL RIGHTS RESERVED ,%33/.)))

9 > i }i2 ELATING THE ,ENGTH OF A 3 OLUTION )NTERVAL TO A #OEFFICIENT n#HANGING THE value OF A COEFFICIENT IN AN absolute value LINEAR INEQUALITY RESULTS IN A CHANGE IN THE SOLUTION INTERVAL 3 OLVE AX B C WHERE A AND C A 3 OLVE THE INEQUALITY FOR X IN TERMS OF A B AND C C B ??????? A X C B ????? A B 6 ERIFY THAT YOUR SOLUTION IS EQUIVALENT TO S B C D ???????? A X C B ????? A 0 OSSIBLE ANSWER 4HE SOLUTION OF THE absolute value INEQUALITY GIVES X C B ????? A AND X C B ??????? A 2 EAD THE SECOND INEQUALITY FROM RIGHT TO LEFT AND COMBINE THE TWO Inequalities INTO A SINGLE INEQUALITY !PPLY THE GENERAL SOLUTION TO SOLVE EACH INEQUALITY X X X X ?

10 ? 2 EFER TO THE Inequalities IN %XERCISES AND A #OMPARE THE VALUES OF A B AND C IN THE TWO Inequalities 4HE VALUES OF B AND C ARE THE SAME IN BOTH Inequalities 4HE value OF A HAS INCREASED FROM THE FIRST INEQUALITY TO THE SECOND B (OW DOES THE value OF A AFFECT THE LENGTH OF THE SOLUTION INTERVAL !S A INCREASES THE LENGTH OF THE SOLUTION INTERVAL DECREASES C 0 REDICT THE SOLUTION INTERVAL FOR THE INEQUALITY X X ?? D 5SE THE GENERAL SOLUTION TO DETERMINE IF YOUR PREDICTION WAS CORRECT ??????? X ????? ??? X ?? X ?? E 7 HAT IS THE RELATIONSHIP BETWEEN THE SOLUTION INTERVAL AND THE COEFFICIENT OF X IN THIS absolute value INEQUALITY 0 OSSIBLE ANSWER 7 HEN THE COEFFICIENT OF X IS DOUBLED THE SOLUTION INTERVAL IS REDUCED BY ?)