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Aim: How do we solve absolute
value equations?
Do Now: Evaluate.
1. | -6 |
2. | 7 |
3. | 2(3)2 – 7(4) |
4. - |3 – 7|
Absolute Value (of x)
• Symbol lxl
• The distance x is from 0 on the number
line.
• Always positive
• Ex: l-3l=3
-4
-3
-2
-1
0
1
2
Ex: x = 5
• What are the possible values of x?
x=5
or
x = -5
To solve an absolute value equation:
ax+b = c, where c>0
To solve, set up 2 new equations, then
solve each equation.
ax+b = c
or
ax+b = -c
** make sure the absolute value is by
itself before you split to solve.
Ex: Solve 6x-3 = 15
6x-3 = 15 or
6x = 18 or
x = 3 or
6x-3 = -15
6x = -12
x = -2
* Plug in answers to check your solutions!
Ex: Solve 2x + 7 -3 = 8
Get the abs. value part by itself first!
2x+7 = 11
Now split into 2 parts.
2x+7 = 11 or 2x+7 = -11
2x = 4 or 2x = -18
x = 2 or x = -9
Check the solutions.
Aim: How do we solve absolute
value inequalities?
• Do Now: Solve.
-3 | 2n – 4 | = -12
Absolute Value Inequalities
• |y|<8
– The solution set is the set of numbers whose
absolute value are less than 8.
– So, -8 < y < 8
• When you have an absolute value inequality
with < or ≤, it will turn into an “AND” problem.
Absolute Value Inequalities,
cont’d
• |y|≥6
– The solution set is the set of numbers whose
absolute value are greater than or equal to 6.
– So, y ≥ 6 or y ≤ -6
• When you have an absolute value
inequality with > or ≥, it will turn into an
“OR” problem.
Solving Absolute Value Inequalities
1. ax+b < c, where c>0
Becomes an “and” problem
Changes to: –c<ax+b<c
2. ax+b > c, where c>0
Becomes an “or” problem
Changes to: ax+b>c or ax+b<-c
Ex: Solve & graph.
4 x  9  21
• Becomes an “and” problem
 21  4x  9  21
12  4x  30
15
3 x 
2
-3
7
8
Solve & graph.
3x  2  3  11
• Get absolute value by itself first.
3x  2  8
• Becomes an “or” problem
3x  2  8 or 3x  2  8
3x  10 or
3x  6
10
x
or x  2
3
-2
3
4
Paired Practice!!!!!