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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

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Inequalities An inequality is a mathematical sentence containing >, <, >, <.

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**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 < >

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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

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**Example 2 The solutions are shown by shading a number line.**

Example: x > 4 3 4 5 6 7

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**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

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1) Graph m > 3 on a number line. 1 2 3 4 5

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

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

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

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**Solving One-Step Inequalities by Adding or Subtracting**

1) x + 4 > 8 x > 4

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**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.

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Graph x > 4 1 2 3 4 5

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**Solving One-Step Inequalities by Adding or Subtracting**

c < 5

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**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.

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**Graph c < 5 on a number line.**

2 3 4 5 6

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**Solving One-Step Inequalities by Adding or Subtracting**

d < 2

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**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.

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Graph d < -2. -5 -4 -3 -2 -1

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**Solving One-Step Inequalities by Adding or Subtracting**

a > 8

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**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.

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Graph a > 8. 5 6 7 8 9

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**Solving One-Step Inequalities by Adding or Subtracting**

p > 7

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**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.

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Graph p > 7 4 5 6 7 8

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**Solving One-Step Inequalities by Adding or Subtracting**

6) j + 5 < 2 j < -3

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**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.

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**Graph j < -3 on a number line.**

-5 -4 -3 -2 -1

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