Lesson 39 Compound and Absolute Value Inequalities NCSCOS 1.01;4.01 Daily Objectives TLW solve compound inequalities. TLW graph the solution sets of compound inequalities. TLW solve absolute value inequalities
Lesson 39 Compound and Absolute Value Inequalities
Jan 02, 2016
Lesson 39 Compound and Absolute Value Inequalities. NCSCOS 1.01;4.01 Daily Objectives TLW solve compound inequalities. TLW graph the solution sets of compound inequalities . TLW solve absolute value inequalities. What is the difference between and and or ?. A. B. AND means intersection - PowerPoint PPT Presentation
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Lesson 39 Compound and Absolute Value Inequalities
NCSCOS 1.01;4.01
Daily ObjectivesTLW solve compound inequalities.
TLW graph the solution sets of compound inequalities.
TLW solve absolute value inequalities
What is the difference between and and or?
AND means intersection-what do the two items
have in common?
OR means union-if it is in one item, it is in
the solution
A
A B
B
1) Graph x < 4 and x ≥ 2
3 42●
a) Graph x < 4
b) Graph x ≥ 23 42
o
c) Combine the graphs
●
3 42o
d) Where do they intersect?●
3 42o
2) Graph x < 2 or x ≥ 4
3 42●
a) Graph x < 2
b) Graph x ≥ 43 42
o
c) Combine the graphs
3 42o
3 42●
3) Which inequalities describe the following graph?
-2 -1-3oo
Answer NowAnswer Now
1. y > -3 or y < -1
2. y > -3 and y < -1
3. y ≤ -3 or y ≥ -1
4. y ≥ -3 and y ≤ -1
When written this way, it is the same thing as
6 < m AND m < 8
It can be rewritten as m > 6 and m < 8 and graphed as previously shown, however,
it is easier to graph everything
between 6 and 8!
4) Graph the compound inequality 6 < m < 8
7 86oo
5) Which is equivalent to-3 < y < 5?
1. y > -3 or y < 5
2. y > -3 and y < 5
3. y < -3 or y > 5
4. y < -3 and y > 5
Answer NowAnswer Now
6) Which is equivalent to x > -5 and x ≤ 1?
1. -5 < x ≤ 1
2. -5 > x ≥ 1
3. -5 > x ≤ 1
4. -5 < x ≥ 1
Answer NowAnswer Now
7) 2x < -6 and 3x ≥ 12
1. Solve each inequality for x
2. Graph each inequality3. Combine the graphs4. Where do they
intersect?5. They do not! x cannot
be greater than or equal to 4 and less than -3 No Solution!!
2 6
2 2 3
x
x
3x 12
3 3 x 4
-3 0-6o
4 71o4 71o
-3 0-6o
8) Graph 3 < 2m + 1 < 9
Remember, when written like this, it is an AND problem!
3 < 2m + 1 AND 2m + 1 < 9
Solve each inequality.
Graph the intersection of 2 < m and m < 3.
0 5-5
9) Graph x < 2 or x ≥ 4
0 5-5
10) Graph x ≥ -1 or x ≤ 3
The whole line is shaded!!
0 5-5
Then graph the solution set.
Write as and
Original inequality
Add 3 to each side.
Simplify.
Case 1 Case 2
Answer: The solution set is
Then graph the solution set.
Answer:
Case 1 Case 2
Then graph the solution set.
Write as or
Add 3 to each side.
Simplify.
Original inequality
Divide each side by 3.
Simplify.
Answer: The solution set is
Then graph the solution set.
Answer:
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