Transcript Thursday, November 18

Thursday, November 18
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Make sure your name is on Practice 3-5 and it is completed!
Today’s objective: SWBAT solve absolute value equations and
inequalities.
Fill in planner with today’s assignment: Practice 3-6
Bell Work (Simplify)
15  15
3  3
12  (12)  24
 18 12  6
  7  7
10  8  2
  2  (1)  3
An absolute value is…

the distance a number is from zero on a
number line.
Example 1: Solving an Absolute
Value Equation
x  5  11
x  5  5  11 5
x 6
x6
or
x  6
6  5  11???
 6  5  11????
Subtract 5 from both sides to isolate the
variable on one side.
The distance of x from zero has to be
six. For what values is this true?
Do both values work? Check your
solutions.
They both work, so they are both
solutions of the equation.
Example 2: Solving an Absolute
Value Equation
Rule: To solve an absolute value equation in the form A  b , where A
represents a variable expression and b>0, solve A = b and A= -b
2 p  5  11
2 p  5  11
2 p  5  11
2 p  5  5  11 5
Remove absolute value symbol
and separate into two equations
2 p  5  5  11 5
Subtract 5 from both sides
2p  6
Simplify
22p  62
p3
Divide both sides of the
equation by 2
or
p  8
2 p  16
2  2 p  16  2
Do the solutions work?
2 p  5  11
p3
2  3  5  11
6  5  11
11  11
p  8
2  (8)  5  11
16  5  11
11  11
Rule(s)
A  b where A is
To solve an inequality in the form _________,
b  A  b
a variable expression and b>0, solve ________________.
A b
To solve an inequality in the form ___________,
where A
A  b
Ab
is a variable expression and b>0, solve _________or_______.
A b
A b
*Similar rules are true for _______and_________.
Example 3: Solving an absolute
value inequality v  3  4
Follow the rule for
A b
4  v 3 4
4  v3
v 3 4
Split into 2 inequalities
Add 3 to both sides
 43  v 33
Simplify
1  v
Combine the Inequalities
Add 3 to both sides
v 33  43
Simplify
v7
1  v  7
Graph Your Solution
1  v  7
Check Your Solution
Does 0 work?
v 3  4
03  4
3  4
Does 3 work?
33  4
0 4