Download 2. 4 = 3|w|

4.6 Absolute Value Equations and Inequalities
Solving Absolute Value Equations
absolute value -
Ex 1: Solve |a| – 3 = 5
Ex 2: Solve 3|x|= 15
Guided Practice
Solve each equation. Check your solution.
1. |t| - 2 = -1
2. 4 = 3|w| - 2
3. Is there a solution of 2|n| = -15. Explain.
Ex 3: Solve |3c - 6| = 9. Check your solution.
Ex 4: Solve |4d + 8| = 36. Check your solution.
Guided Practice
Solve each equation. Check your solution.
1. |c - 2| = 6
2. |2d| + 3 = 21
3. |7x| = 14
Homework: Pages 237 - 238 # 1-17 odd, 18-20
Solving Absolute Value Inequalities
Absolute value inequalities can be written as compound
inequalities.
|n – 2| < 5
|n – 2| > 5
Ex 3: Solve |y – 5| ≤ 2. Graph the solutions.
Ex 4: Solve |2y – 3| > 7. Graph the solution.
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Solving Absolute Value Inequalities
Get the absolute value expression alone on one side of the
inequality
Use the Addition, Subtraction, Multiplication, and
Division properties to get the absolute value
expression alone on one side of the inequality.
- 6|w - 3| + 6 < - 18
Solve each inequality. Graph the solution.
1. |2n + 3| ≤ 5
2. 5 > |v + 2| + 3
3. 3|2x| ≥ 12
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Ex 4: The ideal diameter of a piston for one type of car is
88.000 mm. The actual diameter can vary from the dial
by at most 0.007 mm. Find the range of acceptable
diameters for the piston.
Guided Practice
1. Solve and graph |w + 2| > 5
2. Solve and graph 3|x + 4| ≤ 15
3. The ideal weight of one type of model airplane engine is
33.86 ounces. The actual weight may vary from the ideal
by at most 0.05 ounce. Find the range of acceptable
weights for this engine.
Homework:
Pages 238 - 239 #25 - 35 odd, 37, 41 - 45, 53, 55, 56