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Turn in Section 8 & 9

This lesson covers the critical steps for solving absolute value equations and inequalities. Students will learn how to isolate the absolute value, break the problem into two equations or inequalities, and identify solutions. The session includes graphing techniques on a number line and a discussion on invalid equations, emphasizing that absolute values cannot be negative. Practice problems will be assigned to reinforce learning, utilizing scratch paper for computations before finalizing answers in set notation.

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Turn in Section 8 & 9

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Presentation Transcript

  1. Turn in Section 8 & 9 Take out spiral notebook

  2. Turn Quiz into INBOX Pick up 6-5 Study Guide Complete #1-9 on scratch paper. Do not write on worksheet until you receive further instructions.

  3. Absolute Value Day 1 Review

  4. Steps for Solving Abs. Value Equations • Isolate the absolute value. • Break into two equations. • Solve each equation. • Write solution set with two values. • Graph on number line.

  5. Invalid Equations The absolute value of a number or expression can never be negative. Example: abs(x – 1) = -2

  6. Absolute Value Day 2 Review

  7. Solving and Graphing Absolute Value Inequalities pg 160 • Isolate the absolute value. • Break into two inequalities. • Sign is the same on first inequality. • Reverse sign on the opposite case. • Graph on the number line. • > OR – shade out • < AND – shaded in between

  8. Solving and Graphing Absolute Value Inequalities • GreatOR than is an OR statement • Shade out • Less thAND is an AND statement • Shade in between

  9. Empty Set • Abs (x – 1) < -4 • Absolute value cannot be less than a negative number. • Empty set – no solution

  10. All real numbers • Abs (x + 5) > - 8 • Absolute value is ALWAYS greater than a negative number. • All real numbers.

  11. Additional Notes • +- notation: see white board • Set notation x < 5 AND x > 1 is {x: 1 < x < 5} m > -1 OR m < -7 is {m: m > -1 or m < -7}

  12. 6-5 Study Guide #1-9 Complete #1-9 on scratch paper. Only final answer in set notation and graph go on the worksheet. Accuracy Grade

  13. Section 9 Only 3, 4, 7, 8, 11, 12

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