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Lesson 5: Absolute Value Equations & Inequalities
KEY CONCEPTS
Absolute value - the absolute value of a real number, x , written ๐ฅ๐ฅ , is its distance from zero on the number line.
Extraneous solution - a solution derived from an original equation that is not a solution of the original equation.
Solutions of Absolute Value Statements Concept Summary
Symbols Definition Graph
The distance from x to 0 is a units.
The distance from x to 0 is less than a units.
The distance from x to 0 Is greater than a units.
Solving an Absolute Value Equation
EX #1: Solve each equation. Graph the solution.
A. ๐ฅ๐ฅ โ 6 = 2
B. โ5๐ฅ๐ฅ = 20
C. 3๐ฅ๐ฅ + 2 = 4
D. 2 ๐ฅ๐ฅ + 9 + 3 = 7
B. 7 โ ๐ฅ๐ฅ โค 3
C.
1 4
EX #4: Solve. 5๐ฅ๐ฅ + 10 > 15, graph the solution.
Can you explain what you know?
Without solving ๐ฅ๐ฅ โ 3 โฅ 2 , describe the graph of its solution.
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Writing Absolute Value Statements
EX #5: Write each compound inequality as an absolute value inequality.
A. 1.6 โค ๐ฅ๐ฅ โค 2.1 B. 140 โค ๐๐ โค 230
EX #6: Write an absolute value equation or inequality to describe each graph.
A. B.
