Download 6.4 Solve Compound Inequalities Learning Target Today we will

6.4 Solve Compound Inequalities
Learning Target
Today we will learn to solve compound
inequalities. Think of compound sentences.
Compound inequalities are needed to solve
real life problems involving minimums and
maximums. You will have mastered this
target when you can write, solve, and graph
compound inequalities.
Jan 2­8:28 AM
P.O.D.
Solve and graph the solution to
8 > -x- 4.
Jan 2­8:39 AM
You estimate that you can read at least 8
history textbook pages per day. What are
the possible numbers of days it will take
you to reas at most 118 pages?
Jan 2­8:41 AM
1
Compound Inequalities
A compound inequality consists of two
separate inequalities joined by and or or.
Translate the verbal phrase into an inequality. Then graph
it.
All real numbers that are greater than -2
and less than 3.
Jan 2­8:43 AM
All real numbers that are less than 0 or
greater than or equal to 2.
Jan 2­8:48 AM
The graph of an inequality with and is the
intersection of the graphs of the inequalities.
-2 < x and x < 1
-2 < x < 1
Jan 2­8:49 AM
2
The graph of an inequality with or is the
union of the graphs of the inequalities.
x < -1 or x > 0
Jan 2­8:52 AM
Guided Practice
Translate the verbal phrase into an
inequality. Then graph.
All real numbers that are less than -3 or
greater than or equal to 5.
Jan 2­8:53 AM
All real numbers that are greater than or
equal to -3 and less than 2.
Jan 2­8:56 AM
3
Application Problem
A crane sits on top of a flatbed truck and
faces toward the front. The crane's
maximum height above the ground is 18 feet
and the crane's minimum height above the
ground is 4 feet. Write an inequality that
describes the possible heights of the crane.
Jan 2­8:57 AM
Solving Compound Inequalities
A number is a solution of a compound
inequality with and if the number is a
solution of both inequalities.
A number is a solution of a compound
inequality with or if the number is a solution
of at least one of the inequalities.
Jan 2­9:01 AM
Solve
2<x+5<9
Separate the compound inequality into two
inequalities. Then solve each separately.
Jan 2­9:05 AM
4
Solve the inequality. Graph the solution.
Jan 2­9:08 AM
Jan 2­9:10 AM
Jan 2­9:10 AM
5
Jan 2­9:11 AM
You can solve a compound inequality with
and without separating the inequality into
two separate inequalities. Perform the
same operation on both expressions.
Jan 2­9:12 AM
Solve the inequality without separating it
into two separate inequalities.
Jan 2­9:15 AM
6
Solve a compound inequality with or
Solve 2x + 3 < 9 or 3x - 6 > 12
Jan 2­9:17 AM
Guided Practice
Solve the inequality. Graph the solution.
1. -14 < x - 8 < -1
2.
Jan 2­9:21 AM
Solve a multi-step inequality
The Mars Exploration Rovers Opportunity
and Spirit are robots that were sent to
Mars in 2003 in order to gather geological
data about the planet. The temperature at
the landing sites can range from
Write a compound inequality that describes
the possible temperatures in degrees
Fahrenheit.
Jan 2­9:25 AM
7
Solve the inequality you have written. Graph
your solution.
Identify 3 possible temperatures in degrees
Fahrenheit at a landing site.
Jan 2­9:31 AM
Mars has a maximum temperature of
at the equator and a minimum temperature
at the winter pole.
of
Write and solve a compound inequality that
describes the possible temperatures in
degrees Fahrenheit on Mars.
Jan 2­9:33 AM
Closure
Solve the inequality and graph the solution.
Jan 2­9:37 AM
8