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1 – 7 Solving Absolute Value Equations and Inequalities

Learn to solve equations and inequalities involving absolute value, transform them into linear equations, graph solutions, apply in real-life scenarios.

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1 – 7 Solving Absolute Value Equations and Inequalities

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  1. 1 – 7 Solving Absolute Value Equations and Inequalities Objective: CA Standard 1: Students solve equations and inequalities involving absolute value.

  2. The absolute value of x is the distance the number is from 0. Can the absolute value of x ever be negative? No

  3. Solving an absolute value equation The absolute value equation where c > 0, is equivalent to the compound statement.

  4. Solving an Absolute Value Equation Solve: Rewrite the absolute value equation as two linear equations and then solve each linear equation.

  5. An absolute value inequality such as: can be solved by rewriting it as a compound inequality:

  6. Transformation of Absolute Value Inequalities

  7. Solving an inequality of the form ax + b< c The solution is all real numbers greater than –9 and less than 2. Graph the solution interval.

  8. -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

  9. Solving an inequality of the form ax + b  c This absolute value inequality is equivalent to

  10. The solutions are all real numbers less than or equal to –2 and greater than or equal to 10/3. Draw the graph of the solutions. Are the dots open or closed? Why?

  11. Using Absolute Value in Real life In manufacturing applications, the maximum deviation of a product from some ideal or average measurement is called a tolerance.

  12. Writing a Model for Tolerance A cereal manufacturer has a tolerance of 0.75 ounces for a box of cereal that is supposed to weigh 20 ounces. Write and solve an absolute value inequality that describes the acceptable weights for “20 ounce” boxes. Verbal Model: Actual Weight – Ideal weight Tolerance

  13. Labels: Actual weight = x Ideal weight = 20 Tolerance = .75 Algebraic Model:

  14. Writing an Absolute Value Model You are a quality control inspector at a bowling pin company. A regulation pin weighs between 50 and 58 ounces. Write an absolute value inequality describing the weights you should reject. Verbal Model: Wt. of pin – Avg. wt. of extreme weights  Tolerance

  15. Labels: Weight of pin = w Average weight of extreme weights Tolerance: 58 – 4 = 4

  16. Algebraic Model: You should reject a bowling pin if its weight w satisfies

  17. HOMEWORK:

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