Upload
ami
View
115
Download
3
Embed Size (px)
DESCRIPTION
Solving Absolute Value Equations & Inequalities. Solving Absolute Value Equations & Inequalities. Standard. MM2A1c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology. Absolute Value (of x). Symbol lxl - PowerPoint PPT Presentation
Citation preview
Solving Absolute Solving Absolute Value Equations & Value Equations &
InequalitiesInequalitiesSolving Solving Absolute Absolute
Value Value Equations & Equations & InequalitiesInequalities
MM2A1c. Solve absolute value equations and inequalities analytically, graphically, and by
using appropriate technology.
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-3 = -15
6x = 18 or 6x = -12
x = 3 or 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.
Your Turn: Solve 2x - 5 = 9
How do you solve absolute value inequalities?
First, isolate the absolute value expression on the left side of the inequality
Then choose the form of your inequality
ax b c ax b c ax b c ax b c
Rewrite as
ax+b < c
And
ax+b > -c,
solve for x
Rewrite as
ax+b ≤ c
And
ax + b > -c,
solve for x
Rewrite as
ax + b > c
Or
ax + b < -c,
solve for x
Rewrite as
ax + b ≥ c
Or
ax + b ≤ -c,
solve for x
Solve Solve 4 2 22x 2 5 19x
Ex: Solve & graph.
• Becomes an “and” problem
2194 x
219421 x30412 x
2
153 x
-3 7 8
Solve & graph.
• Get absolute value by itself first.
• Becomes an “or” problem
11323 x
823 x
823or 823 xx63or 103 xx
2or 3
10 xx
-2 3 4
Your Turn: Solve & graph.
2 4 5 15x
Homework:Homework: