Ch 16 Absolute Value Equations and Inequalities EQ How can you solve absolute value equations and inequalities I Will solve absolute value equations and inequalities Bell Work Solve the inequality Graph the solution ID: 593793
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Slide1
Expressions, Equations and Inequalities
Ch. 1.6Absolute Value Equations and Inequalities
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide2
Bell Work
Solve the inequality. Graph the solution.
1. -18-5y
>
522. 4(x+3) < 44
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide3
Absolute Value Equations and Inequalities
READ
Absolute value is of central importance in mathematics itself. As a rule, absolute value equations have two solutions, representing two points on a number line that are at the same distance from a certain number. For inequalities, there are two possible situations depending on the sign of the inequality (see key concept on pg. 41).
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide4
Solving Inequalities
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/absolute-value-equations/v/absolute-value-equations-example-1
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide5
Solving an A
bsolute Value Equation
What is the solution of |2x – 1| = 5? Graph the solution.
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide6
Solving an Absolute Value Equation
Now you try…
What is the solution of |3x+2| = 4? Graph the solution.
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide7
Solving a multi-step absolute value equation
What is the solution of 3|x+2| -1 =
8? Graph the solution.
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide8
Solving a multi-step absolute value equation
Now you try…
What is the solution of 2|x+9| + 3 = 7? Graph the solution.
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide9
Checking for Extraneous Solutions
Extraneous solution- solution derived from an original equation that is not a solution of the original equation.
What is the solution of |3x + 2| = 4x + 5? Check for extraneous solutions.
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide10
Checking for Extraneous Solutions
Now you try…What is the solution of |5x-2| = 7x+14? Check for extraneous solutions.
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide11
Solving the Absolute Value Inequality |A| < b
What is the solution of |2x-1|< 5? Graph the solution.
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide12
Solving the Absolute Value Inequality |A|< b
Now you try…
What is the solution of |3x-4|
<
8? Graph the solution. EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide13
Solving the Absolute Value Inequality |A|
> b
What is the solution of |2x +4|
>
6?EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide14
Solving the Absolute Value Inequality |A| >
b Now you try…
What is the solution of |5x+10| > 15? Graph
the solution.
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. Slide15
Closure
Explains what it means for the solution of an equation to be extraneous.
EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities.