Luttrell 2012
91
Name: ______________________
Date: _____
6g – Linear Inequalities
The solution to a linear inequalit
y
is a set of points that make the inequalit
y
true. In the case of
the inequalit
y
, the solutions include points that lie on one side of the line. The points on the line,
the boundar
y
to half-planar solutions, are solutions onl
y
if the inequalit
y
includes an =. Use the
following e
x
ample as a guide.
E
x
ample: 6
x
+ 3
y
> 12
3
y
> 12 - 6
x
y
> 4 - 2
x
Plot some points on the line
y
= -2
x
+ 4.
Connect the dots with a dashed line since the line itself contain
no solution to the inequalit
y
. Now pick a point that does NOT
lie on the line. (0,0) is an eas
y
choice. Since 0 + 0 > 12 is
false, then the other side of the dashed line must contain the
solutions. Shade the solution side.
Graph the solutions.
1. -2
x
-
y
> 4
2. 3
x
+
y
> 5
3.
x
-
y
> 4
4. -2
x
+
y
≤4
5.
x
+ 2
y
≥ 5
6. 4
x
- 3
y
< 9
