2.6 solve compound inequalitiesorecreek.hartlandschools.us/subsites/annette-macfarlane...notes...
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Notes 2.5.notebook
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October 17, 2017
Warm-up: Solve each inequality, if possible.1. 2x + 4 < 2(x - 6) 2. 6x + 3 > 6x - 5
1.) solve compound inequalities in one variable .2.) graph solutions of compound inequalities in one variable.3.) write a compound inequalitiy by looking at a graph.4.) write a compound inequality from a real world situation.
2.6 Solve Compound InequalitiesI can...
Notes 2.5.notebook
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October 17, 2017
2.6 Solve Compound InequalitiesA compound inequality consists of
TWO separate inequalities joined by and or or.
–2 < x < 2 x ≤ –2 OR x ≥ 2 All real numbers greater than –2 All real numbers less than or equal to –2
AND less than 2 OR greater than or equal to 2
Hint: Always use < or < as long as the smaller number (minimum) is on the left and the larger number (maximum) is on
the right!
The graph of a compound inequality
with and is the intersection
of the graphs of the inequalities.
The graph of a compound inequality
with or is the union of the graphs
of the inequalities.
Example 1: Write an inequality that is represented by the graph.a. b.
2.6 Solve Compound Inequalities♦ I can write a compound inequality by looking at a graph ♦
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Example 2: An iguana needs to live in a warm environment. The temperature in a pet iguana’s cage should be between 70°F and 95°F inclusive. Write a compound inequality to show the temperatures that are within the recommended range. Graph the solutions.
2.6 Solve Compound Inequalities♦ I can write a compound inequality from a real world situation ♦♦ I can graph solutions of compound inequalities in one variable ♦
Checkpoint: The minimum speed on a highway is 40 miles per hour and the maximum speed is 60 miles per hour. Write and graph a compound inequality that describes this situation.
2.6 Solve Compound Inequalities♦ I can write a compound inequality from a real world situation ♦♦ I can graph solutions of compound inequalities in one variable ♦
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Example 3: Solve a compound inequality and graph your solution.
15 < –7x + 1 < 50
2.6 Solve Compound Inequalities♦ I can solve compound inequalities in one variable ♦
Partner Check: Solve and graph each compound inequality.2. –12 < y – 8 ≤ –7 3. 16 > –4y ≥ –4
2.6 Solve Compound Inequalities♦ I can solve compound inequalities in one variable ♦
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October 17, 2017
Example 4: Solve 5x + 6 ≤ −9 or 2x − 8 > 12. Graph your solution.
2.6 Solve Compound Inequalities♦ I can solve compound inequalities in one variable ♦
Checkpoint. Solve the compound inequality and graph your solution. 4. 9x +1 < −17 or 7x − 12 > 9 5. 10x – 3 < –23 or 4 – 3x < –5
2.6 Solve Compound Inequalities♦ I can solve compound inequalities in one variable ♦