Course 2: InequalitiesObjectives: •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 2The solutions are shown by shading a number line. Example: x > 4

3 4 5 6 7

Example 1Determine whether each number is a solution of

a) 3

x 7.

b) -2c) 9

d) 7

yes, because 3 is less than 7yes, because -2 is less than 7no, because 9 is not less than or equal to 7yes, 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.

2 3 4 5 6

Graph c < 5 on a number line.

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.

-5 -4 -3 -2 -1

Graph j < -3 on a number line.

Review