1. Bell Work 1. 2(x +4) 2. 10 – 5(9n – 9) 3. 3(x – 6) + 4 + 8x
Answers:
2x+ 8
11x – 14
Simplify the expression:
1. 2(x +4)
2. 10 – 5(9n – 9)
3. 3(x – 6) x
55 – 45n or – 45n + 55

2. The Distributive Property, Combining Like Terms and Equations

3. Generating Equivalent Expressions Sprint Round 1
Generating Equivalent Expressions Sprint Round 1! You have 2 ½ minutes to complete as many problems as possible. We will grade it right afterwards to see how many you got right.

4. Solving Multi-Step Equations
How can you get the “unknown” by itself?
8x - 3x - 10 = 20
Solving Multi-Step Equations
STEP 1- Combine like terms.
STEP 2- “Undo” addition and/or subtraction.
STEP 3- “Undo” multiplication and/or division.
STEP 4- Solve for the variable.
STEP 5- Check your work.

5. Solving Multi-Step Equations…
Isolate the variable! Get ‘x’ by itself.
8x – 3x – 10 = 20
5x – 10 = 20
Combine like terms.
5x – 10 = 20
Add 10 to each side.
5x = 30
Simplify. = 30 5 5x
Divide each side by 5.
x = 6
Simplify.

6. 8x – 3x – 10 = 20 x = 6 8(6) – 3(6) – 10 = 20 Check Your Work!
8(6) – 3(6) – 10 = 20
Are both sides equal?

7. Solving equations by combining like terms
FIRST, SIMPLIFY BY COMBINING LIKE TERMS ON EACH SIDE OF THE EQUAL SIGN. THEN, SOLVE AS USUAL
7j j – 5 = 40
= 40
9j – 5
9j = 45
j = 5

8. Rewrite the problem, and everywhere you see a j, put in a 5
Check Your Work!!!
Rewrite the problem, and everywhere you see a j, put in a 5
7(5) + 2(5) – 5 = 40
7j + 2j – 5 = 40
– 5 = 40
45 – 5 = 40
40 = 40

9. Check Your Work You Try! z = 8 8z – 4 – 10z = – 20
Rewrite the problem. Everywhere you see a z, put in an 8
– 2z – = – 20
8z - 10z =
8 (8) (8) = -20 =
= - 20
– 2z = – 16
– – 2
= - 20
z = 8
- 20 = - 20

10. – 46 –46 2a = –48 Try another: –4a + 23 + 6a + 23 = – 2 2 2
Combine the like terms on the same side of the equal sign first… –4a with +6a and +23 with +23
2a = – 2
– –46
2a = –48
a = – 24
Check –4(–24) (–24) = –2
– = – 2

11. Try this one! Don’t forget to check your work Example –6x – 8x = 7
Combine the like terms –6x and –8x first...
–14x = 7
Now, solve...
– –14
– 1 2
x =
You can check the original problem...
–6(–1/2) – 8(–1/2) = 7
3 – (– 4)
= 7

12. Solving a Multi-Step Equation
Solving Multi-Step Equations
STEP 1 - Distributive Property
STEP 2- Combine like terms.
STEP 3- “Undo” addition and/or subtraction.
STEP 4- “Undo” multiplication and/or division.
STEP 5- Solve for the variable.
STEP 6- Check your work.

13. Solving Multi-Step Equations Using the Distributive Property…
6x – 2(x – 5) = 46
Distributive property.
6x – 2x + 10 = 46
Combine like terms.
4x + 10 = 46
Subtract 10 from each side.
4x + 10 = 46
– 10 – 10
Simplify.
4x = 36
Divide each side by 4. = 4x 4 36
Simplify.
x = 9

14. x = 9 6(9) – 2(9 – 5) = 46 Check Your Work! Are both sides equal?
6x – 2(x – 5) = 46
x = 9
6(9) – 2(9 – 5) = 46
Are both sides equal?

15. Extra Examples 6x – 2x + 11 = -5 p – 17p – 6 = -38 -16p – 6 = -38

16. Extra Examples 6x – 2(x + 11) = -6 6x + (-2x) + (-22) = -6

17. Extra Examples 27 = 3c – 3(6 – 2c) 27 = 3c + (-18) + 6c

18. PRACTICE