7th Grade Math

Inequalities

Words • is less than

• is fewer than
  
  
  • is greater than
  
  
  • is more than
  
  
  • exceeds
    
    
    • is less than or
      equal to
    
    
    • is no more than
    
    
    • is at most
      
      
      • is greater than
        or equal to
      
      
      • is no less than
      
      
      • is at least
        Symbols <>≤≥
      
      
      
      
    
    
    
    
  
  
  
  

Solve Inequalities

Solve x + 3 > 10.

x + 3 > 10 Write the inequality.

• 3 - 3 Subtract 3 from each side.
  x > 7 Simplify.
  Therefore, the solution is x > 7.

Solve - 6 ≥ n - 5.

• 6 ≥ n - 5 Write the inequality.
  
  
  • 5 + 5 Add 5 to each side.
    
    
    • 1 ≥ n Simplify.
      The solution is - 1 ≥ n or n ≤ -1.
    
    
    
    
  
  
  
  

Solve each inequality.

a. a - 3 < 8 b. 14 + y ≥ 7

Graph Solutions of Inequalities

Solve a + _^1

2

< 2. Graph the solution set on a number line.

a + _^1

2

< 2 Write the inequality.

• _^1
  2
  
  
  • ^1
    2
    Subtract ^12 from each side.
  
  
  
  

a < 1 _^1

2

Simplify.

The solution is a < 1 _^1

2

. Check your solution.
Graph the solution.

• 101234

Place an open dot at. Draw

a line and an arrow to the left.

(^112)
Solve each inequality. Graph the solution set on a number line.
c. h + 4 > 4 d. x - 6 ≤ 4
Open and Closed Dots Open and Closed Dots
When graphing inequalities,
an open dot is used when
the value should not be
included in the solution, as
with > and < inequalities.
A closed dot indicates the
value is included in the
solution, as with ≤ and ≥
inequalities.
Checking Solutions Checking Solutions
To check Example 1, write
the inequality, replace x
with a value in the solution
set, and check to see if
the result is a true
statement.
x + 3 > 10
8 8 + 3  10
11 11 > 10 ✓
Lesson 4B Inequalities 245
242_253_C04L4_895130.indd 245 12/31/09 4:05 PM