 # Course 2: Inequalities Objectives:

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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 < > Words - is less than - is greater than
-is less than or equal to - is at most is greater than or equal to is at least Symbols < >

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 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 1

3) Graph h > 3 on a number line. 1 2 3 4

4) Graph k < -2 on a number line. -3 -2 -1 1

Solving One-Step Inequalities by Adding or Subtracting
1) x + 4 > 8 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
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
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
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
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 j < -3

Check j + 5 < 2 Solution: j < -3
Substitute a value that is less than or equal to -3 for c. < 2 2 < 2  This is a true statement.

Graph j < -3 on a number line.
-5 -4 -3 -2 -1

Review