1. Equations and Inequalities Quick Review
Quick guide to solving Equations and Inequalities

2. Tips:
Remember equations have one solution and inequalities have a solution set (multiple solutions)
You solve two-step equations/inequalities by undoing one operations at a time.
First undo Addition/Subtraction (if the term is being added you subtract , if the term is being subtracted you add)
Second undo the Multiplication/Division (if the term is being added you subtract , if the term is being subtracted you add)
Goes to 0

3. Solving One-Step Equations
Adding
Subtracting
Remember like terms need to go together and you add if the term is subtracted
Remember like terms need to go together and you subtract if the term is added

4. Solving One-Step Equations
Multiplying
Dividing
Remember like terms need to go together and you multiply if the term is divided
Remember like terms need to go together and you divide if the term is multiplied

5. Solving Two-Step Equations
Remember undo Addition/Subtraction the undo Multiplication/Division
Add 7 to both sides
Divide by 2 on both sides
Done!

6. Solving Multi-Step Equations
Remember combine like terms undo Addition/Subtraction the undo Multiplication/Division
Combine like terms 2n and 9n
Add 7 to both sides
Divide by 11 on both sides
Done!

7. Solving Equations w/ Variable on both sides
Combine like terms 2n and 9n add 9n to both sides
Add 7 to both sides
Divide by 11 on both sides
Done!

8. Inequalities
Quick Review

9. Read, Write, and Graph Less Than Less Than or equal to Greater Than
Greater Than or equal to

10. Solving One-Step Inequalities
Adding
Subtracting
Remember like terms need to go together and you add if the term is subtracted
Remember like terms need to go together and you subtract if the term is added

11. Checking One-Step Inequalities
Adding
Subtracting
Check: Pick a number in the solution set
Check: Pick a number in the solution set
Any number less than or equal to 22 is in the solution set
Any number less than or equal to 8 is in the solution set

12. Solving One-Step Inequalities
Multiplying
Dividing
Don’t forget to flip the sign When you multiply or divide by a negative number
Don’t forget to flip the sign When you multiply or divide by a negative number

13. Checking One-Step Inequalities
Multiplying
Dividing
Check: Pick a number in the solution set
Check: Pick a number in the solution set
Any number greater than 75 is in the solution set
Any greater than 3 is in the solution set

14. Compound Inequalities
Rewrite with variable first
“or”
“and”

15. Solving Two-Step Inequalities
Remember undo Addition/Subtraction the undo Multiplication/Division
Add 7 to both sides
Divide by 2 on both sides
Done!

16. Checking Two-Step Inequalities
Remember undo Addition/Subtraction the undo Multiplication/Division
Check: Pick a number in the solution set
Any number less than or equal to 11 is in the solution set

17. Solving Two-Step Inequalities
Remember undo Addition/Subtraction the undo Multiplication/Division
Add 7 to both sides
Divide by -2 on both sides
Remember to flip the sign when multiplying or dividing by a negative number

18. Checking Two-Step Inequalities
Remember undo Addition/Subtraction the undo Multiplication/Division
Check: Pick a number in the solution set
Any number less than or equal to 11 is in the solution set

19. Solving Multi-Step Inequalities
Remember combine like terms undo Addition/Subtraction the undo Multiplication/Division
Combine like terms 2n and 9n
Add 7 to both sides
Divide by 11 on both sides
Done!

20. Checking Multi-Step Inequalities
Check: Pick a number in the solution set
Any number less than or equal to 11 is in the solution set

21. Solving Inequalities w/ Variable on both sides
Combine like terms -2n and 9n subtract 9n to both sides
Add 7 to both sides
Divide by -11 on both sides
Flip the sign
Done!

22. Checking Inequalities w/ Variable on both sides
Check: Pick a number in the solution set
Any number less than or equal to 11 is in the solution set

23. Get common denominators
Example:
Remember to put the variable first