1 – 7 Solving Absolute Value Equations and Inequalities Objective: CA Standard 1: Students solve equations and inequalities involving absolute value.
The absolute value of x is the distance the number is from 0. Can the absolute value of x ever be negative? No
Solving an absolute value equation The absolute value equation where c > 0, is equivalent to the compound statement.
Solving an Absolute Value Equation Solve: Rewrite the absolute value equation as two linear equations and then solve each linear equation.
An absolute value inequality such as: can be solved by rewriting it as a compound inequality:
Transformation of Absolute Value Inequalities
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.
Solving an inequality of the form ax + b c This absolute value inequality is equivalent to
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?
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.
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
Labels: Actual weight = x Ideal weight = 20 Tolerance =.75 Algebraic Model:
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
Labels:Weight of pin = w Average weight of extreme weights Tolerance: 58 – 4 = 4
Algebraic Model: You should reject a bowling pin if its weight w satisfies
HOMEWORK: