1. Objectives:
Solve & graph one-step equations & inequalities by adding or subtracting.

2. Inverse Operations
To solve equations we isolate (get by itself) variables by using inverse operations.
The following needs to be memorized:
Inverse Operations
Addition
Subtraction
Multiplication
Division
Square x2
Square Root

3. Steps to solving ALL equations
Clear parenthesis (Use distributive Property)
Combine Like Terms on each side of the =
Move all variables to one side of the “=“ using inverse operations (+ or -)
Move all constants (numbers) to the other side of the “=“ using inverse operations (+ or -)
Get rid of the constant (number) attached to the variable by either (x or ÷)

4. = z – 1 2 5
y – 8 = 24 + 1 2
y = 32
= z
5.5
m + 17 = 33
–11 + x = 33.
– 17 –17
m = 16
x = 44

5. The following symbols need to be memorized….
When graphing inequalities the symbol tells you what type of dot you should have.
Hint: If there is a solid line under the symbol you should have a solid dot!

6. Before graphing an inequality make sure that your variable is on the LEFT side. If this is true the arrow should point in the same direction as the symbol.
Symbol points LEFT,
Arrow points LEFT
Symbol points RIGHT,
Arrow points RIGHT

7. Flip the numbers, flip the sign.
If the variable is on the right….
Flip the numbers, flip the sign.
Example: > x becomes x < 6

8. 5. Graph x < 7
6. Graph -3 < x

9. 7. Graph x ≥ -2
8. Graph 4 ≤ x

10. All inequalities have an infinite number of solutions.
ANY number that falls on the arrow is considered a solution.
Example: –4 –3 –2 –1 1 2 3 4 5 6
Solutions: 0, -1, -2, -3, -1000, -10,000,000…
NOT solutions: 1, 2, 3, 4, 5, ….

11. If you have an OPEN dot… that number is NOT a solution. Example:

12. x + 12 < 20 x < 8 d – 5 > –7 +5 +5 d > –2
Solve the inequality and graph the solutions. 9.
10.
x + 12 < 20
– –12
x < 8
–10 –8 –6 –4 –2 2 4 6 8 10
d – 5 > –7
d > –2
–10 –8 –6 –4 –2 2 4 6 8 10

13. Solve the inequality and graph the solutions.
11.
12.
s + 1 ≤ 10
–1 –1
s ≤ 9 9
–10 –8 –6 –4 –2 2 4 6 8 10
-5 ≤ y +2
– –2
–10 –8 –6 –4 –2 2 4 6 8 10
-7 ≤ y
y ≥ -7