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Solving Absolute Value Inequalities
This document discusses how to solve absolute value equations. It defines absolute value as the distance from 0, which is always non-negative. To solve absolute value equations, you treat it as two separate equations by removing the absolute value signs and solving each equation separately. The total solutions are the solutions from both equations. The document provides examples of solving single-step and multi-step absolute value equations. It explains the process is similar to solving linear equations, by undoing operations outside the absolute value signs first.
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Introduction to absolute value equations defining absolute value as distance from zero.
Cautions about negative values in absolute equations; examples illustrating solutions with multiple outcomes.
Process for solving multi-step absolute value equations, including examples for practice.
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Solving Absolute Value Inequalities
- 1. Solving Absolute ValueEquationsGoals: Solve equations involving absolute valuesRewrite absolute value inequalities in compound form and solve
- 2. DefinitionThe absolute valueof a number, x, is the distance the number is from 0.Since distance is nonnegative, the absolute value of a number is always nonnegative.x, if x is positive
- 3. DefinitionThe absolute valueof a number, x, is the distance the number is from 0.Since distance is nonnegative, the absolute value of a number is always nonnegative.x, if x is positive0, if x is 0
- 4. DefinitionThe absolute valueof a number, x, is the distance the number is from 0.Since distance is nonnegative, the absolute value of a number is always nonnegative.x, if x is positive0, if x is 0-x, if x is negative
- 5. If you takethe negative of an absolute value,Then your answer becomes negative.!!!CAUTION!!!
- 6. , then thex can be equal If theto either 6 or -6.Therefore, when taking the absolute value of an equation, there are TWO possible solutions:ORAbsolute Value Equations
- 7. Now solve bothequations separately:Write your solutions together:x = -7 or 3Absolute Value Equations
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- 10. EXAMPLES:1)2)3)4)x = -2or 8x = -6 or 1
- 11. EXAMPLES:1)2)3)4)x = -2or 8x = -6 or 1x = -10 or -6
- 12. EXAMPLES:1)2)3)4)x = -2or 8x = -6 or 1x = -10 or -6-11 2x = -4 or
- 13. The way tosolve multi-step absolute value equations is like solving a multi-step linear equation.Instead of solving by isolating the variable by undoing 1st: addition/subtraction 2nd: multiplication/divisionYou isolate the absolute value by undoing 1st: addition/subtraction outside the abs. value 2nd: multiplication/division outside the abs. valueMulti-Step Absolute Value Equations
- 14. Walk-Through: Solvethe following -7 3x = 3 or
- 15. x = -12or -2Walk-Through: Solve the following
- 16. Solve the followingabsolute value equations:1)2)3)Try the Following On Your Own:
- 17. Solve the following:1)x= or 42)3) -2 3Solutions:
- 18. Solve the following:1)x= or 42)x = or 3) -2 3 -9 2 19 2Solutions:
- 19. Solve the following:1)x= or 42)x = -1 or 63)x = -6 or 0 -2 3Solutions: