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 - 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 + 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 + 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 + 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 + 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