2.1 Writing and Graphing Inequalities
2.1 Writing and Graphing Inequalities
COMMON CORE
Learning Standard HSA-CED.A.1
ATTENDING TO PRECISION
To be proficient in math, you need to communicate precisely. You also need to state the meanings of the symbols you use.
Essential Question How can you use an inequality to describe a
real-life statement?
Writing and Graphing Inequalities
Work with a partner. Write an inequality for each statement. Then sketch the graph of the numbers that make each inequality true. a. Statement The temperature t in Sweden is at least -10?C.
Inequality
Graph
-40 -30 -20 -10 0 10 20 30 40
b. Statement The elevation e of Alabama is at most 2407 feet.
Inequality
Graph
-3000 -2000 -1000
0
1000 2000 3000
Writing Inequalities
Work with a partner. Write an inequality for each graph. Then, in words, describe all the values of x that make each inequality true.
a.
-4
-3
-2
-1
0
1
2
3
4
b.
-4
-3
-2
-1
0
1
2
3
4
c.
-4
-3
-2
-1
0
1
2
3
4
d.
-4
-3
-2
-1
0
1
2
3
4
Communicate Your Answer
3. How can you use an inequality to describe a real-life statement?
4. Write a real-life statement that involves each inequality. a. x < 3.5 b. x 6 c. x > -2 d. x 10
Section 2.1 Writing and Graphing Inequalities
53
2.1 Lesson
Core Vocabulary
inequality, p. 54 solution of an inequality, p. 55 solution set, p. 55 graph of an inequality, p. 56 Previous expression
What You Will Learn
Write linear inequalities. Sketch the graphs of linear inequalities. Write linear inequalities from graphs.
Writing Linear Inequalities
An inequality is a mathematical sentence that compares expressions. An inequality contains the symbol , , or . To write an inequality, look for the following phrases to determine what inequality symbol to use.
Symbol
Key Phrases
<
is less than
is fewer than
Inequality Symbols
>
is greater is less than or is greater than
than
equal to
or equal to
is more than
is at most
is at least
is no more than is no less than
READING
The inequality 3 < n + 5 is the same as n + 5 > 3.
Writing Inequalities
Write each sentence as an inequality. a. A number w minus 3.5 is less than or equal to -2. b. Three is less than a number n plus 5. c. Zero is greater than or equal to twice a number x plus 1.
SOLUTION a. A number w minus 3.5 is less than or equal to -2.
w - 3.5
-2
An inequality is w - 3.5 -2.
b. Three is less than a number n plus 5.
3
<
n + 5
An inequality is 3 < n + 5.
c. Zero is greater than or equal to twice a number x plus 1.
0
An inequality is 0 2x + 1.
2x + 1
Monitoring Progress
Help in English and Spanish at
Write the sentence as an inequality.
1. A number b is fewer than 30.4. 2. ---170 is at least twice a number k minus 4.
54
Chapter 2 Solving Linear Inequalities
Sketching the Graphs of Linear Inequalities
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 -7 -8
x + 5 -2
-6 + 5 ? -2
-1 -2
? -7 + 5 -2
-2 -2 -8 + 5 ? -2
-3 -2
Is the inequality true? yes yes no
Recall that a diagonal line through an inequality symbol means the inequality is not true. For instance, the symbol means "is not greater than or equal to."
Checking Solutions
Tell whether -4 is a solution of each inequality. a. x + 8 < -3 b. -4.5x > -21
SOLUTION
a. x + 8 < -3 -4 + 8 ................
................
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