Transcript Notes

7.5
Linear Inequalities
7.5 – Linear Inequalities
Goals / “I can…”
Graph linear inequalities
Write and use linear inequalities when modeling
real – world situations
7.5 – Linear Inequalities
RECALL
Graph x > 4 on a number line.
-4
-2
0
2
4
Graph y ≤ 2 on a number line.
-4
-2
0
2
4
7.5 – Linear Inequalities
REMEMBER:
The type of dot on the number line is
important.
Open DOT means NOT INCLUDED (> or <)
Closed DOT means INCLUDED (≤ or ≥)
Remember these symbols!!!!




Less than
Greater than
Less than or EQUAL TO
Greater than or EQUAL TO
7.5 – Linear Inequalities
When graphing inequalities on the
coordinate plane, we use a similar idea.
Dashed lines mean the same as open circles.
 (> or <)
Solid lines mean the same as closed circles.
 (≤ or ≥)
Graphing an Inequality in Two Variables
Graph x < 2
Step 1: Start by graphing
the line x = 2
Now what points
would give you less
than 2?
Since it has to be x < 2
we shade everything to
the left of the line.
7.5 – Linear Inequalities
Oh, and did I mention we have to shade a
part of the graph?????
When considering shading, you shade the
part of the graph that WORKS FOR THE
EQUATION.
Graphing a Linear Inequality
Sketch a graph of y  3
7.5 – Linear Inequalities
Graph
x≥3
7.5 – Linear Inequalities
Graph
y ≤ 2x + 2
Solving an Inequality
Solving a linear inequality in one variable is much like
solving a linear equation in one variable. Isolate the
variable on one side using inverse operations.
Solve using addition:
x–3<5
Add the same number to EACH side.
x 3  5
+3
+3
x<8
Solving Using Subtraction
Subtract the same number from EACH side.
x  6  10
-6
-6
x4
THE TRAP…..
When you multiply or divide each side of
an inequality by a negative number, you
must REVERSE the inequality SYMBOL
to maintain a true statement.
Solving by multiplication of a negative
#
Multiply each side by the same negative number
and REVERSE the inequality symbol.
(-1)
 x  4 (-1)
Multiply by (-1).
See the switch
x  4
Solving by dividing by a negative #
Divide each side by the same negative
number and reverse the inequality symbol.
 2x  6
-2
-2
x3
Solving using Multiplication
Multiply each side by the same positive number.
1
(2)
x  3 (2)
2
x6
Some Helpful Hints
•If the sign is > or < the line is
dashed
•If the sign is  or  the line will be
solid
When dealing with just x and y.
•If the sign > or  the shading
either goes up or to the right
•If the sign is < or  the shading
either goes down or to the left
Using What We Know
Sketch a graph of x + y < 3
Step 1: Put into
slope intercept form
y < -x + 3
Step 2: Graph the
line y = -x + 3
When dealing with slanted lines
•If it is > or  then you shade above
•If it is < or  then you shade below
the line