Graphing and Solving Inequalities. Finding an Inequality Boundary Boundary Point: A solution(s) that...
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Transcript of Graphing and Solving Inequalities. Finding an Inequality Boundary Boundary Point: A solution(s) that...
Graphing and Solving Inequalities
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 5 1x
To find a boundary replace the inequality
symbol with an equality symbol.
2 5 1x 2 6x
3x
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
Reminder: Compound Inequalities
The following are examples to algebraically write the following graphs:
0 4
0≤x<4
-1 2
x<-1 or x>2
Solving a 1 Variable Inequality
2 22 5 3 4 3x x x x
2 22 5 3 4 3x x x x 2 6 0x x
3 2 0x x
3 or 2x x
0
x
x = -4 x = 0 x = 3
9 ≤ 3 -3 ≤ 3 30 ≤ 24False True False
Find the Boundary Test Every Region
3 2x
Represent the solutions to the following inequality algebraically and on a number line.
2 22 4 5 4 3 4 4 4 3 2 2
2 3 5 3 3 3 4 3 3 2 2
2 0 5 0 3 0 4 0 3
Change inequality to equality
Solve
Plot Boundary Point(s)
Pick a point in each region
Substitute into Original
Shade True Region(s) Algebraic
Solution
Closed or Open Dot(s)?
Graphical Solution
Solving a 2 Variable Inequality
(0,0)
Graphically represent the solutions to the following inequality.
Find the Boundary
32 3y x
32 3y x
Plot points for the equality
Test Every Region
(3,0)
0 > -3 0 > 1.5
True False
320 0 3 3
20 3 3
Solid or Dashed?
Pick a point in each region
Substitute into Original
Shade True Region(s)
Reminder: Cover-Up Method
Plot : -2x + 5y = -10Find the
intercepts
X Y
00 -25
If the graph is in Ax+By=C
form.
Solution to a System of Inequalities
A solution to a System of Inequalities is the coordinate(s) that makes ALL of the inequalities true. The graph of all the points that make the system true is called the Feasible Region.
EX: Prove (-4,5) is a solution to the system below2 6
3 7
x y
x y
It must make
EVERY inequality
true. 2 4 6 5
8 6 5 14 5
3 4 7 5 12 7 5
19 5True True
Solving a System of Inequalities
2
2
2 5 3
4 3
y x x
y x x
(0 ,0)
0 ≥ -3True
(0 ,0)
0 < 3True
Test Every Region
Graphically represent the solutions to the following system of inequalities:
Find the Boundaries
2 4 3y x x Plot points for the equalities one at a time
22 5 3y x x
Solid or Dashed?
0 1 3x x 0 2 1 3x x
Find which side to shade for each inequality
20 0 5 0 3 2
0 0 4 0 3
Shade the Feasible Region