Transcript Slide 1

Solving Absolute Value
Equations
MATH 018
Combined Algebra
S. Rook
Overview
• Section E.1 in the textbook
– Definition of Absolute Value
– Solving Absolute Value Equations
– Isolating the Absolute Value
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Definition of Absolute Value
Definition of Absolute Value
• Absolute Value: distance from 0 as
viewed on a number line
– Thus can only be positive or 0
• How would we solve |X| = a where a > 0?
X = a or X = -a
{a, -a} (written in set notation)
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Definition of Absolute Value
(Continued)
• How would we solve |X| = 0?
X = 0 → {0}
• If |X| = a where a < 0, what is the solution?
{ } or Ø, but NEVER {Ø}
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Definition of Absolute Value
(Example)
Ex 1: Solve:
a) |x| = 7
b) |y| = 0
c) |z| = -1
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Solving Absolute Value
Equations
Solving Absolute Value
Equations
• Recall the number of solutions:
– If |X| = a where a > 0, then X = a or X = -a
• Two solutions
– If |X| = 0, then X = 0
• One solution
– If |X| = a where a < 0, then X = { }
• No solution
• Same thing applies when an expression is
inside the absolute value bars
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Solving Absolute Value Equations
(Example)
Ex 2: Solve:
a) |w – 3| = 8
b) |5 – 3y| = 0
c) |z + 6| = -3
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Isolating the Absolute Value
Isolating the Absolute Value
• Before applying the definition of absolute
value, the absolute value must be
ISOLATED first
– VERY important!
– The absolute value must be ISOLATED
before the definition of absolute value can be
applied!
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Isolating the Absolute Value
(Example)
Ex 3: Solve:
a) 4|3x – 2| – 3 = -1
b) |y + 1| + 4 = -5
c) z  1 1
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
3
 2  2
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Summary
• After studying these slides, you should know
how to do the following:
– Know the definition of absolute value and apply it to
solve simple equations
– Solve more complicated absolute value equations
– Isolate the absolute value before solving an equation
• Additional Practice
– See the list of suggested problems for E.1
• Next lesson
– Rectangular Coordinate System (Section 3.1)
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