Transcript 1.7 Solving Absolute Value Equations & Inequalities

Solving Absolute Value
Equations & Inequalities
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.
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.
4x  9  21
• Becomes an “and” problem
 21  4 x  9  21
 12  4 x  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
3 x  10 or
3 x  6
10
x
or x  2
3
-2
3
4
Assignment