1. Preview of Grade 7 AF Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations, or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
California
Standards

2. Vocabulary inequality algebraic inequality solution set
compound inequality

3. Symbol Meaning Word Phrases
An inequality is a statement that compares two expressions by using one of the following symbols: <, >, ≤, ≥, or .
Symbol
Meaning
Word Phrases
<
> ≤ ≥
is less than
Fewer than, below
is greater than
More than, above
is less than or equal to
At most, no more than
is greater than or equal to
At least, no less than

4. Additional Example 1: Writing Inequalities
Write an inequality for each situation.
A. There are at least 15 people in the waiting room.
“At least” means greater
than or equal to.
number of people ≥ 15
B. The tram attendant will allow no more
than 60 people on the tram.
“No more than” means
less than or equal to.
number of people ≤ 60

5. Check It Out! Example 1
Write an inequality for each situation.
A. There are at most 10 gallons of gas in the tank.
“At most” means less
than or equal to.
gallons of gas ≤ 10
B. There is at least 10 yards of fabric left.
“At least” means
greater than or equal to.
yards of fabric ≥ 10

6. An inequality that contains a variable is an algebraic inequality
An inequality that contains a variable is an algebraic inequality. A value of the variable that makes the inequality true is a solution of the inequality.
An inequality may have more than one solution. Together, all of the solutions are called the solution set.
You can graph the solutions of an inequality on a number line. If the variable is “greater than” or “less than” a number, then that number is indicated with an open circle.

7. a > 5 b ≤ 3 This open circle shows that 5 is not a solution.
If the variable is “greater than or equal to” or “less than or equal to” a number, that number is indicated with a closed circle.
This closed circle shows that 3 is a solution.
b ≤ 3

8. Additional Example 2: Graphing Simple Inequalities
Graph each inequality.
Draw an open circle at 3. The solutions are values of n less than 3, so shade to the left of 3.
A. n < 3
–3 –2 –
B. a ≥ –4
Draw a closed circle
at –4. The solutions are –4 and values of a greater than –4, so shade to the right of –4.
–6 –4 –

9. Check It Out! Example 2 Graph each inequality.
Draw a closed circle at 2. The solutions are 2 and values of p less than 2, so shade to the left of 2.
A. p ≤ 2
–3 –2 –
B. e > –2
Draw an open circle
at –2. The solutions are values of e greater than –2, so shade to the right of –2.
–3 –2 –

10. x is either greater than 3 or less than–1.
A compound inequality is the result of combining two inequalities. The words and and or are used to describe how the two parts are related.
x > 3 or x < –1
–2 < y and y < 4
x is either greater than 3 or less than–1.
y is both greater than –2 and less than y is between –2 and 4.
The compound inequality –2 < y and y < 4 can be written as –2 < y < 4.
Writing Math

11. Additional Example 3: Graphing Compound Inequalities
Graph each compound inequality.
A. m ≤ –2 or m > 1
Graph m ≤ –2
Graph m > 1 • 2 4 6 – 2 4 6 –2 –4 –6
Include the solutions shown by either graph. 1 2 3 4 5 6 –

12. Additional Example 3: Graphing Compound Inequalities
Graph each compound inequality.
B. –3 < b ≤ 0
Graph –3 < b
Graph b ≤ 0 • 2 4 6 –2 –4 –6 2 4 6 –
Include the solutions that the graphs have in common. 1 2 3 4 5 6 –

13. Graph each compound inequality.
Check It Out! Example 3
Graph each compound inequality.
A. w < 2 or w ≥ 4
Graph w < 2
Graph w ≥ 4 2 4 6 – 2 4 6 –2 –4 –6
Include the solutions shown by either graph. 1 2 3 4 5 6 –

14. • º Check It Out! Example 3 Graph each compound inequality.
B. 5 > g ≥ –3
Graph 5 > g
Graph g ≥ –3 • 2 4 6 –2 –4 –6 2 4 6 –
Include the solution that the graphs have in common. 1 2 3 4 5 6 –