1.6 absolute value equations and inequalities students will be able to: write and solve equations...
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1.6 – Absolute Value Equations and Inequalities An absolute value equation has a variable within the absolute value sign. For example, |x| = 5. Here, the value of x can be 5 or -5 since |5| = 5 and |-5| = 5.TRANSCRIPT
1.6 – Absolute Value Equations and Inequalities
Students will be able to:•Write and solve equations and inequalities
involving absolute value.
Lesson Vocabulary•Absolute value
•Extraneous solution
1.6 – Absolute Value Equations and Inequalities
An absolute value quantity is nonnegative. Since opposites have the same absolute value,
an absolute value equation CAN have two solutions.
1.6 – Absolute Value Equations and Inequalities
An absolute value equation has a variable within the absolute value sign. For example,
|x| = 5. Here, the value of x can be 5 or -5 since |5| = 5 and |-5| = 5.
1.6 – Absolute Value Equations and Inequalities
Problem 1:What is the solution of |2x – 1| = 5?
Graph the solution.
1.6 – Absolute Value Equations and Inequalities
Problem 1b:What is the solution of |3x +2| = 4?
Graph the solution.
1.6 – Absolute Value Equations and Inequalities
Problem 1c:What is the solution of |5x +2| = -7?
Graph the solution.
1.6 – Absolute Value Equations and Inequalities
Problem 2:What is the solution of 3|x +2| - 1 = 8?
Graph the solution.
1.6 – Absolute Value Equations and Inequalities
Problem 2b:What is the solution of 2|x +9| +3 = 7?
Graph the solution.
1.6 – Absolute Value Equations and Inequalities
An extraneous solution is a solution derived from an original equations that is NOT a
solution of the original equation.
1.6 – Absolute Value Equations and Inequalities
Problem 3:What is the solution of |3x +2| = 4x + 5?
Check for extraneous solutions!
1.6 – Absolute Value Equations and Inequalities
Problem 3b:What is the solution of |5x - 2| = 7x + 14?
Check for extraneous solutions!
1.6 – Absolute Value Equations and Inequalities
The solutions of the absolute value inequality|x| < 5 include values greater than -5 and less
than 5. This is a compound inequality x>-5 and x<5, which you can write as
-5 < x < 5. So |x| < 5 means x is BETWEEN -5 and 5.
1.6 – Absolute Value Equations and Inequalities
Problem 4:What is the solution of |2x - 1| < 5?
Graph the solution.
1.6 – Absolute Value Equations and Inequalities
Problem 4b:What is the solution of |3x - 4| < 8?
Graph the solution. Is this an “and” problem or an “or” problem?
1.6 – Absolute Value Equations and Inequalities
Problem 5:What is the solution of |2x +4| > 6?
Graph the solution. Is this an “and” problem or an “or” problem?
1.6 – Absolute Value Equations and Inequalities
Problem 5b:What is the solution of |5x +10| > 15?
Graph the solution. Is this an “and” problem or an “or” problem?
1.6 – Absolute Value Equations and Inequalities
Problem 5c:Without solving |x – 3| > 2, describe the graph
of its solution.
1.6 – Absolute Value Equations and Inequalities
A manufactured item’s actual measurements and its target measurements can differ by a
certain amount, called tolerance. Tolerance is one half the difference of the maximum and minimum acceptable values. You can use
absolute value inequalities to describe tolerance.
1.6 – Absolute Value Equations and Inequalities
Problem 6:In car racing, a car must meet specific dimensions to enter the race. Officials use a template to ensure these specifications are met. What
absolute value inequality describes heights of the model race car shown within the indicated tolerance?
1.6 – Absolute Value Equations and Inequalities
Exit Ticket:
Explain what it means for a solution of an equation to be extraneous.
When is the absolute value of a number equal to the number itself?
Give an example of a compound inequality that has no solution.