Transcript Solving Compound Inequalities Continued…

Solving Compound
Inequalities Continued…
Example 1
Warm-up
Translate the verbal phrase into an inequality. Then
graph the inequality.
All real numbers that are greater than –2 and less
than 3
1. Inequality:
2. Graph:
All real numbers that are less than 0 or greater than
or equal to 2
3. Inequality:
4. Graph:
Example 1
Warm-up
Translate the verbal phrase into an inequality. Then
graph the inequality.
All real numbers that are greater than –2 and less
than 3
1. Inequality: –2 < x < 3
2. Graph:
All real numbers that are less than 0 or greater than
or equal to 2
3. Inequality: x < 0 or x  2
4. Graph:
Let’s Review…
Compound Inequality
– two separate
inequalities join by
and or or.
OR
Union of the
graphs of the
inequalities
AND
Must answer
either of the
inequalities
Intersection
of the graphs
of the
inequalities.
Must answer
both
inequalities.
Example 2
CAMERA CARS
A crane sits on top of a
camera car and faces toward
the front. The crane’s
maximum height and
minimum height above the
ground are shown. Write and
graph a compound inequality
that describes the possible
heights of the crane.
All possible heights are greater than or equal to 4 feet and
less than or equal to 18 feet. So, the inequality is 4  h  18.
Solve: 2x < -6 and 3x ≥ 12
Solve each inequality
Graph each solution
Where do they intersect?
They do not!
No Solution!!
Æ
2 x 6

2
2
x  3
o
-3
3x 12

3
3
x4
-6
1
o
●
4
0
7
Solve:
3x+2 < 2 or 1-x ≥ 4
3x < 0
-x ³ 3
x <0
x £ -3
●
o
-1
0
-4
1
-3 -2
Unite the two sets
Solution : x < 0
-3
0
5
Graph x > -1 or x < 3
-1 0
3
The entire number line is shaded!!
What is the solution???
{all real numbers}
Guided Practice
Solve the inequality, if possible. Graph your solution.
6 – x ≤ 4 and 4x + 9 < -3
n + 19 ≥ 10 or -5n + 3 > 33
Solve and graph
Using logic with inequalities