Transcript Inequalities

Solving and Graphing
Linear Inequalities
DIRECTIONS
1. Read the worksheet to see what questions
you will have to answer before you continue
with this PowerPoint.
2. Read the entire PowerPoint but don’t
answer the questions yet.
3. Go through the PowerPoint again and
answer the questions.
What’s an inequality?
Symbols





Less than
Greater than
Less than OR EQUAL TO
Greater than OR EQUAL TO
NOT equal to
Solutions….
A solution set is the set of numbers that
satisfy an equation or inequality.
The solution set can be show as a graph:
-5 -4 -3 -2 -1 0
1
2
3
in words: All real numbers less than 2
or in set notation: {x|x< 2}
4
5
Solutions continued…
-5 -4 -3 -2 -1 0
1
2
All real numbers greater than -2
x > -2
3
4
5
Solutions continued….
-5 -4 -3 -2 -1 0
1
2
3
4
5
All real numbers less than or equal to 1
x 1
Solutions continued…
-5 -4 -3 -2 -1 0
1
2
3
4
5
All real numbers greater than or equal to -3
x  3
Did you notice,
Some of the dots were solid
and some were open?
x2
-5 -4 -3 -2 -1
0
1
2
3
4
5
-5 -4 -3 -2 -1
0
1
2
3
4
5
x 1
Why do you think that is?
If the symbol is > or < then dot is open because it can not be
equal.
If the symbol is  or  then the dot is solid, because it can be
that point too.
Graphing Inequalities





Less than: circle shade left
Greater than: circle shade right
Less than or equal to: dot shade left
Greater than or equal to: dot shade right
Not equal to: circle shade both directions
Solving an Inequality
Solving a linear inequality in is much like solving a linear equation. The
differences are:
1. You graph the solution set for an inequality.
2. You must flip the inequality sign if you multiply or divide by
a negative number.
x–3<5
Solve using addition:
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 using Multiplication
Multiply each side by the same positive number.
1
(2)
x  3 (2)
2
x6
Solving Using Division
Divide each side by the same positive number.
3x  9
3
3
x3
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