Download Solving a Linear Inequality

Solving a Linear Inequality
Solving an Inequality
In order to find the points that satisfy an
inequality statement:
1.
Find the boundary
2. Test every region to find which one(s)
satisfies the original statement
Finding an Inequality Boundary
Boundary Point: A solution(s) that makes the
inequality true (equal). It could be the smallest
number(s) that make it true. Or it is the largest
number(s) that makes it NOT true.
EX: Find the boundary point of 2 x  5  3
To find a boundary replace the
inequality symbol with an equality
symbol.
2x  5  3
2x  8
x4
Solving a 1 Variable Inequality
Represent the solutions to the following inequality
algebraically and on a number line.
Closed or Open Dot(s)?
3  2x  1
Find the Boundary
Test Every Region
Graphical
Solution
x
Change inequality to equality
Solve
3  2x  1
2 x  2
x 1
Plot Boundary Point(s)
0
Pick a point in
each region
x=0
Substitute
into Original
Shade True
Region(s)
x=2
3  2  0  1 3  2  2  1
3<1
False
x 1
-1 < 1
True
Algebraic
Solution
Solving a 1 Variable Inequality: The Answer
is All Numbers
Represent the solutions to the following inequality
algebraically and on a number line.
Closed or Open Dot(s)?
9k  4  1  2k  3  7k
Find the Boundary
Graphical
Solution
Test Every Region
x
Change inequality to equality
9k  4  1  2k  3  7k
0
Solve
9k  3  9k  3
00
Since every value of k satisfies the
equation, every Point is a Boundary Point
All Numbers
“Algebraic”
Solution
Solving a 1 Variable Inequality: No Solutions
Represent the solutions to the following inequality
algebraically and on a number line.
Closed or Open Dot(s)?
3y 1  3y 1
Find the Boundary
Graphical
Solution
Test Every Region
x
Change inequality to equality
3y 1  3y 1
Solve
0
00
Since every value of k satisfies the
equation, every Point is a Boundary Point
No Solution
“Algebraic”
Solution