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Recall that absolute value of a number is that number's distance from zero on the number line. Use the above definition to solve the following: x = - case 1 |x|=7 Type in your answer(s). case 2 x= + The first step to solving an absolute value equation is to determine if the absolute value expression is isolated. Why? Because there is nothing on the outside of the absolute bars - before or after. |-5x-1| |2x+4| Isolated |x+5| |7x| |x| Click "OK" to go to the next slide. Why? Because of what's highlighted in red. 5 NOT Isolated |x+8| |x-3| 4 |x+2| |3x| 2 |x| +12 -6 +2 Add to both sides The absolute value expression is now isolated |4x|-9=11 |x|+6=12 Use the inverse operation(s) if an absolute value equation is NOT isolated. -6 -6 |x|=6 What will it take to isolate the absolute value expression? Type in your answer(s). Divide both sides by The absolute value expression is now isolated 2|x|=16 2 2 5|x|=25 |x|= 8 Click "OK" to go to the next slide. x+4=-9 case 1 -4 -4 x=-13 Step 2: Once the absolute value expression has been isolated,the definition of absolute value can be applied. |x+4|=9 Split the equation into 2 cases andsolve for x using inverse operations x+4=+9 case 2 -4 -4 x=+5 Isolated? YES! 2x-4=-12 case 1 +4 +4 2x=-8 2 2 x=-4 |2x-4|=12 2x-4=+12 case 2 +4 +4 2x=+16 2 2 x=+8 Dropped the bars and made one equal to -9 and the other to +9 x+4=-9 case 1 -4 -4 x=-13 Solutions to the equation Used inverse operation |x+4|=9 Type in your answers from SMALLEST to LARGEST. Did you see how the definition of the absolute value was applied? x+4=+9 case 2 -4 -4 x=+5 Isolated? YES! Now SPLIT! 2x-5= x= case 1 Now complete the problem by using inverse operations Now you try one! |2x-5|=15 2x-5= x= case 2 Solve the following equation: Now that we have broken down all the steps to solving an absolute value equation, let's solve one from scratch. 4x= x= |4x|- 6 = 34 case 1 |4x| = 4x= case 2 x= Step 1: Isolate the absolute value expression by using inverse operations Step 2: Split into 2 cases Step 3: Solve using inverse operation(s) Type in your answer(s) x= Try this one totally on your own: |x+2| - 5 = 8 Type in your answer from SMALLEST to LARGEST. Remember: Isolate, Split, Solve x= x= Try this one totally on your own: Type in your answer from SMALLEST to LARGEST. Remember: Isolate, Split, Solve 3|x+2| = 18 x= |x|= There is a special case. It occurs . If the absolute value expression , there will be . number -7 Here are some example: |3x+6|= Click "OK" to go to the next slide. |x-3|= All of these equations have NO SOLUTION NO SOLUTION -5 -4 is equal to a negative after the isolation |7x|= -2 Solve the following equation: |3x + 5| + 9 = 3 How many solutions did you find? Try this one on your own. No solution 1-solution 2-solutions Choose the best answer. Remember to isolate first! |