You already know that equations are mathematical statements that describe two expressions with equal values. When the values of the two expressions are not equal, their relationship can be described in an inequality.
Verbal phrases like greater than or
less than describe inequalities. For example, 6 is greater than 2.
This is the same as saying 2 is less than 6.
The chart below lists other phrases
that indicate inequalities and their corresponding symbols.
1. Suppose the minimum driving age in your state is 16. Write an inequality to describe people who are not of legal driving age in your state.
Alternative Solutions:
Let d
represent the ages of people who are not of legal driving age.
Then d is
less than 16, or d = 16.
Not only can inequalities be
expressed through words and symbols, but they can also be graphed.
Consider the
inequality d ≥ 16.
The graph shows all values that are greater than or equal
to 16.
Now suppose we want to graph all
numbers that are less than 16. We want to include all numbers up to 16,
but not including 16.
The graph shows all values that are less than 16
Example
Graph each inequality on a number line.
2. x > –4
Alternative Solutions:
Since x cannot equal –4, graph a circle at –4 and shade to the right.
3. n ≥ 1.5
Alternative Solutions:
Since n can equal 1.5, graph a bullet at 1.5 and shade to the right.
You can also write inequalities given their graphs.
Example
Write an inequality for each graph.
Alternative Solutions:
Locate where the graph begins. This graph begins at 1, but 1 is not included. Also note that the arrow is to the left. The graph describes values that are less than 1.
So, x <
1
Alternative Solutions:
Locate where the graph begins. This graph begins at ¼ and includes 1 4. Note that the arrow is to the right. The graph describes values greater than or equal to ¼.
So, x ≥
¼.
Inequalities are commonly used in the
real world.
Sports
Link
6. To play junior league soccer, you
must be at least 14 years of age.
A. Write an inequality to represent this situation.
Alternative Solutions:
Let a represent the ages of people who can play junior league soccer. Then write an inequality using since the soccer players have to be greater than or equal to 14 years of age.
a ≥ 14
B. Graph the inequality on a number line.
Alternative Solutions:
To
graph the inequality, first graph a bullet at 14. Then include all ages greater
than 14 by drawing a line and an arrow to the right.
C. The Valdez children are 10, 13, 14, and 16 years old. Which of the children can play junior league soccer?
Alternative Solutions:
The
set of the children’s ages, {10, 13, 14, and 16}, can be called a replacement
set. It includes possible values of the variable a. In this case, only 14 and
16 satisfy the inequality a ≥ 14 and are members of the solution set.
So, the two Valdez children that are 14 and 16 years old can play junior league
soccer.
Sumber
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