Transcript Solving and Graphing Inequalities

Warm Up
Solve the equation.
1. x  2  5
2. 4 x  2  10
3. x  3  6  8
4. 2 x  9  3  7
5. 6  3 2 x  1  15
answers
1.
2.
3.
4.
5.
x
x
x
x
x
=
=
=
=
=
7 and x = -3
3 and x = -2
5 and x = 1
-2 ½ and x = -6 ½
1 and x = -2
3.5
Solving and Graphing
Inequalities
► What
is an
inequality?
► What
are the
inequality
signs?
► An
inequality is a statement that
shows how two expressions
compare, using greater than or
less than symbols.




greater th an
less than
greater th an or equal to
less than or equal to
Exploration
► Write
each pair of numbers,
write an inequality symbol to
compare them, and perform
the indicated steps.
► Add four to each side.
Compare the answers.
► Subtract five from each side.
Compare the answers.
5
8
5 < 8
9 < 12
4 < 7
Exploration
► Write
each pair of numbers,
write an inequality symbol to
compare them, and perform
the indicated steps.
► Add ten to each side.
Compare the answers.
► Subtract seven from each
side. Compare the answers.
-3
-8
-3 > -8
7 > 2
0 > -5
What did you notice?
► Summarize
what you noticed about the
inequality sign after performing the
indicated operations.
 Adding or subtracting the same number to both
sides of the inequality does not change the
inequality sign.
Exploration
► Write
each pair of numbers,
write an inequality symbol to
compare them, and perform
the indicated steps.
► Multiply by four on each side.
Compare the answers.
► Divide by two on each side.
Compare the answers.
4
-12
4 > -12
16 > -48
8 > -24
Exploration
► Write
each pair of numbers,
write an inequality symbol to
compare them, and perform
the indicated steps.
► Multiply by negative two on
each side. Compare the
answers.
► Divide by negative four on
each side. Compare the
answers.
-6
10
-6 < 10
12 > -20
-3 < 5
What did you notice?
► Summarize
what you noticed about the
inequality sign after performing the
indicated operation.
 Multiplying or dividing by a positive number on
both sides does not affect the inequality sign.
 Multiplying or dividing by a negative number on
both sides changes the direction of the
inequality sign.
► Steps
for Solving
an Inequality
1)
2)
3)
4)
5)
Distribute
Combine like terms
Move the variable to one
side
Undo addition or
subtraction
Undo multiplication or
division (if mult. or div. by
a neg. change sign)
► Steps
for
Graphing an
Inequality
Draw a number line
including the number in
the solution.
2) Draw a circle around the
value in the solution.
3) Fill in the circle if the
value is a part of the
solution, leave it open if it
is not part of the solution.
4) Draw an arrow in the
direction of the values in
the solution.
1)
Examples
Solve and graph each inequality.
4 5 6 7
x
>
6
1) x + 7 > 13
2)
-21 > x - 18
-3 > x
x < -3
8 9
-5 -4 -3 -2 -1 0
Examples
Solve and graph each
inequality.
n  -12
n
3)
4
3
►
4)
50  5 x
10  x
x  10
-14
-14
-12
-12
-10
-10
Examples
Solve and Graph
5) 2x + 1 > 13
- 1 -1
2x > 12
2
2
X >6
6) 7 – 2t > 21
-7
-7
-2t > 14
-2 -2
t < -7
-9
0
2
4
6
8
-7
-5
-3
-1 0
Try These: solve and graph
7. 3 – 3x + 2 > 5 – 2x
8. 4m – 4 < 2 + 4m
9. -3(x – 2) < 3 – (2x + 4)
Answers
7. 0 > x
0
8. I.M.S
9. 7 < x
7
Summary/Reflection
► How
is solving an inequality alike and
different from solving an equation?
► How will you remember which direction to
draw the arrow on the graph?
► How will you remember whether to use an
open or closed circle?
Homework
► Worksheet
3.5