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Absolute-Value Equations and Inequalities

Absolute-Value Equations and Inequalities. Mental Math Solving. Think  What values could x be that would make the equation true? HINT: There are two! ANSWER: 5 or -5. Mental Math Solving (More Example).  x = 7 or -7  x = 9 or -9  x = 18 or -18. Solving an Absolute-Value Equation.

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Absolute-Value Equations and Inequalities

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  1. Absolute-Value Equations and Inequalities

  2. Mental Math Solving • Think  What values could x be that would make the equation true? HINT: There are two! • ANSWER: 5 or -5

  3. Mental Math Solving (More Example) •  x = 7 or -7 •  x = 9 or -9 •  x = 18 or -18

  4. Solving an Absolute-Value Equation • This means that can equal 5 or -5. x – 2 IS NEGATIVE x – 2 IS POSITIVE SOLUTION: x = 7 or x = -3

  5. Solving an Absolute-Value Equation 2x – 7 IS POSITIVE 2x – 7 IS NEGATIVE

  6. POSITIVE NEGATIVE

  7. IMPORTANT CHEAT SHEET Solving Absolute-Value Equations and Inequalities ax+b<c means ax+b<c AND ax+b>-c ax+b≤c means ax+b≤cAND ax+b≥-c ax+b=c means ax+b=c OR ax+b=-c ax+b>c means ax+b>c ORax+b<-c ax+b≥c means ax+b≥c ORax+b≤-c

  8. Solving Absolute-Value Inequalities • Remember that is the distance between and 0. • If , then any number between -8 and 8 is solution to the inequality.

  9. x – 4 IS NEGATIVE x – 4 IS POSITIVE

  10. 2x + 1 IS NEGATIVE 2x + 1 IS POSITIVE

  11. POSITIVE NEGATIVE

  12. Notecard Check

  13. Homework Assignment • Pg. 356 – 357 • Numbers: 24 – 36 and 46 – 46 evens

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