Page 496 - Algebra 1

L E S S O N Solving Compound Inequalities 73
Warm Up
New Concepts
1. Vocabulary A(n) __________ is a mathematical statement comparing
(45)
Solve.
2. x + 7 < 0
(66)
4.-x≥5 (70)
quantities that are not equal.
3. x - 3 ≥ -5 (66) _
5. -x ≤3 (70) 4
Sometimes inequalities are described using two inequalities instead of just one. In these instances, a compound inequality is written to represent the situation. A compound inequality is two inequalities combined with the word AND or OR. A conjunction is a compound inequality that uses the word AND.
The statement x ≥ -3 AND x ≤ 5 is a conjunction. Because the word “AND” connects the two inequalities, the conjunction can also be written -3 ≤ x ≤ 5.
The graph of a conjunction is the intersection of the graphs of the two inequalities. That is, it includes all points common to both inequalities. For example, consider the graph of x ≥ -3 AND x ≤ 5.
x ≥ -3 x≤5
-3 ≤ x ≤ 5
-4 -2 0 2 4 6 Common Points
Writing and Graphing Conjunctions
Write and graph a compound inequality to represent the statement.
a. all real numbers that are greater than 1 and less than 4 SOLUTION
Reading Math
Read -3 ≤ x ≤ 5 as “x is greater than or equal to -3 and less than or equal to 5,” or as “x is between -3 and 5, inclusive.”
Example
1
Math Language
The phrase “less than” and “is less than” are often confused. For example, “six less than x” is translates to x - 6 while “six is less than x” translates to 6 < x.
x > 1 AND x < 4 or 1 < x < 4
b. The winds of a hurricane range from 75 miles per hour to 200 miles
0246
Online Connection www.SaxonMathResources.com
per hour.
SOLUTION
x ≥ 75 AND x ≤ 200 or 75 ≤ x ≤ 200
0 50 100 150 200 250
Lesson 73 481