14.1 Lesson
14.1 Lesson
Key Vocabulary inequality solution of an
inequality solution set graph of an inequality
An inequality is a mathematical sentence that compares expressions. It contains the symbols , , or . To write an inequality, look for the following phrases to determine where to place the inequality symbol.
Inequality Symbols
Symbol
<
>
Key Phrases
is less than
is fewer than
is greater than
is more than
is less than or equal to
is at most is no more than
is greater than or equal to
is at least is no less than
EXAMPLE 1 Writing an Inequality
A number w minus 3.5 is less than or equal to -2. Write this sentence as an inequality.
A number w minus 3.5 is less than or equal to -2.
w - 3.5
-2
An inequality is w - 3.5 -2.
Exercises 6 ? 9
Reading
The symbol / means
"is not greater than or equal to."
Write the word sentence as an inequality. 1. A number b is fewer than 30.4. 2. Twice a number k is at least ---7 .
10
A solution of an inequality is a value that makes the inequality true. An inequality can have more than one solution. The set of all solutions of an inequality is called the solution set.
Value of x -6
x + 5 -2 -6 + 5 ? -2
-1 -2
Is the inequality true? yes
-7
-7 + 5 ? -2
-2 -2
yes
-8
-8 + 5 ? -2
-3 / -2
no
98
Chapter 14 Linear Inequalities
EXAMPLE 2 Checking Solutions
Tell whether -4 is a solution of the inequality.
a. x + 8 < -3
b. -4.5x > -21
x + 8 < -3
-4 + 8 ................
................
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