Transcript Solving Absolute Value Equations & Inequalities

Warm Up
Solve each equation for the given variable.
1) 7x = 56
2) 3y + 7 = 19
3) 4 – 2x = 16
4) x – 9 = -22
6-5 Solving Absolute
Value Equations
Standard 3.0: Students solve
equations and inequalities
involving absolute value.
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
Try It Out!
x 7
x  22
x  3.4
To solve an absolute value equation:
ax+b = c, where c>0
*C cannot be negative
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.
Try It Out!
• Solve each equation.
x  3  10
2x  8  6
4n 1  11
7 x  35
Homework Assignment
• Page 325 #7 – 18 All