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- 1. Solving Absolute Value Equations<br />Goals: <br />Solve equations involving absolute values<br />Rewrite absolute value inequalities in compound form and solve<br />
- 2. Definition<br />The absolute value of a number, x, is the distance the number is from 0.<br />Since distance is nonnegative, the absolute value of a number is always nonnegative.<br />x<br />, if x is positive<br />
- 3. Definition<br />The absolute value of a number, x, is the distance the number is from 0.<br />Since distance is nonnegative, the absolute value of a number is always nonnegative.<br />x<br />, if x is positive<br />0<br />, if x is 0<br />
- 4. Definition<br />The absolute value of a number, x, is the distance the number is from 0.<br />Since distance is nonnegative, the absolute value of a number is always nonnegative.<br />x<br />, if x is positive<br />0<br />, if x is 0<br />-x<br />, if x is negative<br />
- 5. If you take the negative of an absolute value,<br />Then your answer becomes negative.<br />!!!CAUTION!!!<br />
- 6. , then the x can be equal <br />If the<br />to either 6 or -6.<br />Therefore, when taking the absolute value of an equation, there are TWO possible solutions:<br />OR<br />Absolute Value Equations<br />
- 7. Now solve both equations separately:<br />Write your solutions together:<br />x = -7 or 3<br />Absolute Value Equations<br />
- 8. EXAMPLES:<br />1)<br />2)<br />3)<br />4)<br />
- 9. EXAMPLES:<br />1)<br />2)<br />3)<br />4)<br />x = -2 or 8<br />
- 10. EXAMPLES:<br />1)<br />2)<br />3)<br />4)<br />x = -2 or 8<br />x = -6 or 1<br />
- 11. EXAMPLES:<br />1)<br />2)<br />3)<br />4)<br />x = -2 or 8<br />x = -6 or 1<br />x = -10 or -6<br />
- 12. EXAMPLES:<br />1)<br />2)<br />3)<br />4)<br />x = -2 or 8<br />x = -6 or 1<br />x = -10 or -6<br />-11<br /> 2<br />x = -4 or<br />
- 13. The way to solve multi-step absolute value equations is like solving a multi-step linear equation.<br />Instead of solving by isolating the variable by undoing<br /> 1st: addition/subtraction<br /> 2nd: multiplication/division<br />You isolate the absolute value by undoing<br /> 1st: addition/subtraction outside the abs. value<br /> 2nd: multiplication/division outside the abs. value<br />Multi-Step Absolute Value Equations<br />
- 14. Walk-Through: Solve the following<br /> -7<br /> 3<br />x = 3 or<br />
- 15. x = -12 or -2<br />Walk-Through: Solve the following<br />
- 16. Solve the following absolute value equations:<br />1)<br />2)<br />3)<br />Try the Following On Your Own:<br />
- 17. Solve the following:<br />1)<br />x = or 4<br />2)<br />3)<br /> -2<br /> 3<br />Solutions:<br />
- 18. Solve the following:<br />1)<br />x = or 4<br />2)<br />x = or <br />3)<br /> -2<br /> 3<br /> -9<br /> 2<br /> 19<br /> 2<br />Solutions:<br />
- 19. Solve the following:<br />1)<br />x = or 4<br />2)<br />x = -1 or 6<br />3)<br />x = -6 or 0<br /> -2<br /> 3<br />Solutions:<br />

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