Course 2: Inequalities
Objectives:
•To determine whether a number is a solution of an
inequality
•To graph inequalities on the number line
•To write inequalities
Inequalities
• An inequality is a mathematical
sentence containing >, <, >, <.
Inequalities
- is less
than
Words
Symbols
<
- is
greater
than
>
-is less
than or
equal to
- is at
most
<
-is
greater
than or
equal to
-is at
least
>
Inequalities
• Any number that makes an inequality
true is a solution of the inequality.
• Inequalities have many solutions.
• Example: x > 4
• List 4 possible solutions. 4.5, 5, 7, 12.5
Example 2
The solutions are shown by shading a number
line.
Example: x > 4
3 4 5 6 7
Example 1
Determine whether each number is a solution
of x  7.
a) 3
yes, because 3 is less than 7
b) -2
yes, because -2 is less than 7
c) 9
no, because 9 is not less than or
equal to 7
d) 7
yes, because 7 is equal to 7
1)
Graph m > 3 on a number line.
1
2
3 4 5
2)
Graph k < -2 on a number line.
-3 -2 -1 0 1
3)
Graph h > 3 on a number line.
0 1
2 3 4
4)
Graph k < -2 on a number line.
-3 -2 -1 0 1
Solving One-Step Inequalities
by Adding or Subtracting
• 1) x + 4 > 8
-4 -4
x>4
Check x + 4 > 8
• Solution: x > 4
• Substitute a value that is greater
than 4 for x.
5+4>8
9 > 8  This is a true statement.
Graph x > 4
1
2
3 4 5
Solving One-Step Inequalities
by Adding or Subtracting
• 2) c - 3 < 2
+3 +3
c<5
Check c – 3 < 2
• Solution: c < 5
• Substitute a value that is less than
or equal to 5 for c.
5–3<2
2 < 2  This is a true statement.
Graph c < 5 on a number line.
2
3 4 5 6
Solving One-Step Inequalities
by Adding or Subtracting
• 3) d - 4 < -2
+4 +4
d<2
Check d – 4 < -2
• Solution: d < 2
• Substitute a value that is less than 2
for d.
1 – 4 < -2
-3 < -2  This is a true statement.
Graph d < -2.
-5 -4 -3 -2 -1
Solving One-Step Inequalities
by Adding or Subtracting
• 4) a - 2 > 6
+2 +2
a>8
Check a - 2 > 6
• Solution: a > 8
• Substitute a value that is greater
than or equal to 8 for a.
8-2>6
6 > 6  This is a true statement.
Graph a > 8.
5 6
7 8 9
Solving One-Step Inequalities
by Adding or Subtracting
• 5) p - 7 > 0
+7 +7
p>7
Check p - 7 > 0
• Solution: p > 7
• Substitute a value that is greater
than 7 for p.
8-7>0
1 > 0  This is a true statement.
Graph p > 7
4 5
6 7 8
Solving One-Step Inequalities
by Adding or Subtracting
• 6) j + 5 < 2
-5 -5
j < -3
Check j + 5 < 2
• Solution: j < -3
• Substitute a value that is less than
or equal to -3 for c.
-3 + 5 < 2
2 < 2  This is a true statement.
Graph j < -3 on a number line.
-5 -4 -3 -2 -1
Review