- This document provides instructions for solving basic 2-step equations by getting the variable term alone on one side of the equation using inverse operations, then solving. It also covers combining like terms by adding coefficients of the same variables or constants. The distributive property and solving multi-step equations by distributing, combining like terms, and then solving is also explained. Examples of each type of equation are worked out.

2. Basic 2-Step Equations 10/1/13
 A lot like 1-step equations!
 Goal: Get x by itself!
 Need to “undo” what is done to x.
 Always do the same thing to BOTH
SIDES!
 Use Order of Operations backwards:
 Add/Subtract first
 Multiply/Divide last

3. Examples:
4x + 7 = 27
– 6 – 2y = 10

4. You Try!
Solve each equation. Check your
answers!
-3x + 7 = 16
-8 = 2a + 2

5. 5 = 7r - 2
-4 = 2 - m

6. Combining Like Terms 10/7/13
 What are “like terms”?
 Must have the same variable, or
have no variable.
 Terms without a variable are called
“constants.”
 Remember: Variables are letters!
 The number before the letter is called
the coefficient.

7.  Which are like terms?
2x – 6 + 9y + 2 – 6x + 2y
To combine like terms:
 Circle, underline, or box the like terms
 Minus signs go with the next #
 Add their coefficients!

8.  Examples:
 Simplify each expression.
 4x + 2 – 2x + 1
 8y – 4 + 3y

9.  -7 + 3m – 4 – m

10. You Try!
 Simplify.
 5x + 3 – 2x + 1

11.  8x – y + 9 – 2y
 a + 2a – 5 + b + 2b

12. You Try!
 Simplify:
 4m – 2n + 9 – 4m – 5

13. The Distributive Property 10/8/13
The distributive property tells us how
to simplify expressions like: 2(x – 1)
We distribute the outside number to
both inside terms.
Like this:
Remember: “ab” means “a times b”

14. Examples:
Simplify.
3(2x + 1)
-2(4 – 3y)

15. You Try!
Simplify.
4(3x + 5)
-6(3 – 2v)

16. More Examples:
 -(-m + 4)
 (1 + 7b)6

17. You Try!
 -(-z + 5)
 (4 – 3y)5

18. Simplifying Expressions
10/9/13
First, distribute to get rid of all
parentheses.
Then, combine like terms.

19. Examples:
Simplify each expression.
3(4n + 2) + n
7x – (2x – 3) + 1

20. You Try!
Simplify each expression.
5(3x + 1) – 4x
4r – 6(1 + r)

21. -2(m + 5) + 6m – 1
4(x + 7) – 2(1 + 5x)

22. You Try!
 -5(2 – b) + 3b – 7
 2(3k + 6) – 4(1 – 2k)

23. Multi-Step Equations 10/14/13
Multi-step equations have more than 2
steps.
To solve:
 Simplify the side with the variables.
Distribute
 Combine Like Terms
 Like terms may NOT cross the = sign!

 Then, solve like a 1 or 2-step equation!

24. Examples:
3(– 6 + 3x) = 18
30 = -5(6n + 6)

25. You Try!
 -6(1 – 5v) = 54

26. Examples:
2x + 3x + 1 = 36
-26 = -7b + 6 + 3b

27. You Try!
8m – 3m + 7 = 17

28. Examples:
-3(1 + 6r) + r = 14

29. 6(6v + 6) – 5 – 6v = 1

30. You Try!
70 = 3(-6y – 5) – 5