1.6 absolute value equations and inequalities. solving an absolute value equation what is the...
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1.6 Absolute Value Equations and Inequalities
Solving an Absolute Value Equation• What is the solution of | 2x – 1 | = 5? Graph the
solution.
| 2x – 1 | = 5
2x – 1 = 5 OR 2x – 1 = -5
2x = 6 2x = -4
x = 3 OR x = -2
Solving a Multi-Step Absolute Value Equation
• What is the solution of 3| x + 2 | - 1 = 8? Graph the solution.
3| x + 2 | - 1 = 8
3 | x + 2 | = 9
| x + 2 | = 3
x + 2 = 3 OR x + 2 = -3
x = 1 x = -5
Checking for Extraneous Solutions• What is the solution of | 3x + 2 | = 4x + 5? Graph
the solution.
| 3x + 2 | = 4x + 5 3x + 2 = 4x + 5 OR 3x + 2 = -(4x + 5) 3x = 4x + 3 3x + 2 = -4x - 5
-x = 3 7x = -7 x = -3 x = -1
• Since x = -3 does not satisfy the original equation, -3 is an extraneous solution. The only solution to the equation is x = -1.
Solving the Absolute Value Inequality | A | < b
• What is the solution of | 2x – 1 | < 5? Graph the solution.
| 2x – 1 | < 5
-5 < 2x – 1 < 5
-4 < 2x < 6
-2 < x < 3
Solving the Absolute Value Inequality | A | ≥ b
• What is the solution of | 2x + 4 | ≥ 6? Graph the solution.
| 2x + 4 | ≥ 6
2x + 4 ≤ -6 OR 2x + 4 ≥ 6
2x ≤ -10 2x ≥ 2
x ≤ -5 OR x ≥ 1
More Practice!!!!!
• Homework – Textbook p. 46 #10 – 36.
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