1. Bell Ringer
x + 7 = x = - 28
x – 11 =

2. Solve Multi-step Equations
4x + 7 ( x – 2 ) = -8
3 ( x – 4 ) = 6
I can solve equations with multiple steps (more than two) using distributive property, combining like terms, and inverse operations.
-3 = 3a + 5 ( a – 9 ) + 4
POWER to the brain.
m – 9 – ( 3m + 4 ) = 1

3. Solving Multi-step equations
Example 1: z + 16 = 51
Step 1: subtract 16 from both sides
Step 2: simplify z = 35
Step 3: divide both sides by
Step 4: solve z = 7
Example 2:
Step 1: add 20 to both sides
Step 2: simplify
Step 3: cross-multiply and divide y = 72
Step 5: solve y = -72

4. Simplifying vs. Solving
Simplifying: Solving:
when combining like when moving terms
terms on same side over the = sign, you of = sign, DO NOT DO change the sign
do the opposite
EX. 3x x = EX. 3x + 5 = 17

5. REVIEW: Simplify Using Combining Like Terms
Like Terms must have the same variables and the same powers on the letters.
Combine like terms by adding or subtracting the coefficients (numbers in front of the variables).
Example 1: 3x + 5 – 7x + 9
-4x
+ 14
Example 2: 3 – 6y – 7 – 9y -4
– 15y

6. Solving Multi-step Equations
Write the original equation.
Combine like terms.
Add 8 to each side.
Simplify.
Divide each side by 4.
Simplify.
CHECK

7. Let’s try these 1.) - 12 = 9x + 15 – 6x 2.) 5f + 4f – 8 = 19
- 27 = 3x
-9 = x
5f + 4f – 8 = 19
9f – 8 = 19
9f = 27
f = 3

8. Time to play bingo!!!!!!!!!

9. REVIEW: Simplify Using the Distributive Property.
Distributive Property – Multiply times everything in the parentheses.
a ( b + c ) =
ab + ac
OR a ( b – c ) =
ab – ac
Example 1: -3 ( x + 5 )
-3x
– 15
Example 2: -7 ( 2a – 4 )
-14a
+ 28

10. Bell Ringer Solve the equations (Copy problem) 1.) + 12 = 15 3x
1.) = 15
2.) 5 – 2x = 13
3.) 9 = 4x + 2 – 2x + 5
4.) 5(2x +8) = 50 3x 4

11. How do we simplify and solve equations with multiple steps?
To solve equations with multiple steps, first use the distributive property to get rid of the parentheses.
Then, combine like terms to get the problem in the 2-step form.
Solve by using inverse operations as you do with 2-step equations.

12. Simplify and Solve Equations
FIRST - Use the Distributive Property to get rid of the parentheses.
Example: 3 ( x – 2 ) + 4x = 8
SECOND: Combine like terms. 3x
– 6
+ 4x = 8
Copy the rest of the problem. 7x
– 6 = 8
Now it’s a regular 2-step equation.
Add 6 to both sides.
7x = 14
Divide both sides by 7.
x = 2
Use your calculator for the computations if needed.

13. Simplify and Solve Example: 3x + 2 ( 2x – 1 ) = 33
Use Distributive Property
2. Combine Like terms
3. Use Inverse Operations
3x = 33 4x
– 2 7x
– 2 = 33
7x = 35
x = 5

15. Simplify and SOLVE: -4y – 5 – 4( -2y – 3 ) + 8 = 3
Distributive Property
- 4y – 5
+ 8y
+ 12
+ 8 = 3
Copy the rest of the problem.
Combine like terms. 4y
+ 7
+ 8 = 3 4y
+ 15 = 3
– 15 – 15
4y = -12
Use your calculator for the computations if needed.
y = -3

16. Distributive Property
Simplify and Solve:
Distributive Property
-5x + 3 – ( 9x – 2 ) + 7 = 96
-5x = 96
– 9x
+ 2
Combine Like Terms
-14x
+ 12
= 96
– – 12
-14x = 84
x = - 6
Use your calculator for the computations if needed.

17. SUMMARY
To solve equations with multiple steps, first use the distributive property to get rid of the parentheses.
Then, combine like terms to get the problem in the 2-step form.
Solve by using inverse operations as you do with 2-step equations.

18. Practice: Multi-step Equations 1
Copy the problems and solve for the variable. Be sure you show all your steps to receive full credit. NO WORK = NO CREDIT
1. 2n + 3n + 7 = -41
2. 2x - 5x = -14.4
3. 2z z = -5.15
4. 3h - 5h + 11 = 17
2t t = -3
6. 6a - 2a = -36
7. 3c - 8c + 7 = -18
8. 7g g = -8
9. 2b b = 14
(a - 4) + 15 = 13
(a - 3) = -9
(5c - 2) = 29
(3x + 12) = -15
(2a + 2) - 17 = 15
(m + 1) = 16
x + 3(2x - 5) = 31
(2k + 4) = 18
(t - 12) = 27
w + 4(w + 3) = -12
= 0.4(3d - 5)
d + 2(3 + d) = -14
x + (4x + 16) = 7
(3a + 2) = -8
(t - 3) - 2t = -30
(b + 4) - 6b = -24
26. (5k + 35) - 8 = 12
(2s + 4) = 4.8
28. (9b - 27) = 36
29. (12n - 8) = 26
(2x - 4) = -17
STOP