1. 5.1 Solving Inequalities by Addition and Subtraction
Objective: Solve Linear inequalities by using addition and subtraction

2. Graphing Inequalities
< or > means open circle
 or  means closed circle

3. Set-Builder Notation
Definition- A more concise way of writing a solution set.
The solution set for Example 1 is
This is read the set of all numbers such that x is greater than or equal to 20.

4. Solve by adding or subtracting
X ≥ 20;
{x | x ≥ 20 }

5. Solve, Graph and Write the solution set.
30 > m or m < 30
{m | m < 30}

6. Solve, Graph and Write the solution set.
-27 < c; { c | c > - 27}

7. Solve, Graph and Write the solution Set
6 ≤ a ; {a | a ≥ 6 }

8. Solve, Graph and Write in set builder notation
D ≥ -5 ; {d | d≥ -19}

9. Solve, Graph and Write the answer in set-builder notation
-1 < n, {n| n > -1}

10. Solve and Write the solution set
H ≥ 12; {h | h ≥ 12}

11. Phrases for Inequalities
<
>  
Less than
Fewer than
Greater Than
More Than
At most, no more than, less than or equal to
At least, no less than, greater than or equal to

12. Write and Graph the Inequality
You must be at least 16 years old to go on the trip.
The sum of a number and -4 is more than 8
Twice a number is less than the sum of that number and 9
The sum of twice a number and 5 is at most that number minus 3
X ≥ 16
H + (-4) > 8 = H > 12
2n > n +9; n > 9
2n + 5 ≤ n - 3 ; n ≤ - 8

13. Word Problem
Sanjay has $65 to spend at the mall. He bought a T-shirt for $18 and a belt for $14. If Sanjay still wants to buy a pair of jeans, how much can he spend?
j ≤ 65
32 + j ≤ 65
J ≤ 33
At most $33

14. Page 286 #36
M + 20 > 61
M > 41
There were originally more than 41 songs on the MP3 Player