Bell Work

Simplify the expression:

1. 2(x +4)

2. 10 – 5(9n – 9)

3. 3(x – 6) + 4 + 8x

Answers:

2x+ 8

11x – 14

55 – 45n or – 45n + 55

The Distributive Property,

Combining Like Terms and Equations

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.

How can you get the “unknown” by itself?

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.

8x - 3x - 10 = 20

Solving Multi-Step Equations…

Isolate the variable! Get ‘x’ by itself.

8x – 3x – 10 = 20

5x – 10 = 20 Combine like terms.

5x – 10 = 20 + 10 + 10 Add 10 to each side.

5x = 30 Simplify.

Divide each side by 5.

x = 6 Simplify.

= 305

5x5

Check Your Work!

x = 6

8(6) – 3(6) – 10 = 20

Are both sides equal?

8x – 3x – 10 = 20

Solving equations by combining like terms

FIRST, SIMPLIFY BY COMBINING LIKE TERMS ON EACH SIDE OF THE EQUAL SIGN. THEN, SOLVE AS USUAL

7j + 2j – 5 = 40

9j – 5 = 40

+5 +5

9j = 45

9 9

j = 5

Check Your Work!!!Rewrite the problem, and everywhere you see a j, put in a 5

7j + 2j – 5 = 40 7(5) + 2(5) – 5 = 40

35 + 10 – 5 = 40

45 – 5 = 40 40 = 40

You Try!

8z – 4 – 10z = – 20

– 2z – 4 = – 20+4 = +4

– 2z = – 16

– 2 – 2

z = 8

Rewrite the problem. Everywhere you see a z, put in an 8

8z - 10z - 4 = - 20 8 (8) - 10 (8) - 4 = -20

64 - 80 - 4 = - 20

- 16 - 4 = - 20

- 20 = - 20

Check Your Work

TRY ANOTHER: –4A + 23 + 6A + 23 = – 2Combine the like terms on the same side of the equal sign first… –4a with +6a

and +23 with +23

2a + 46 = – 2 – 46 –46

2a = –48 2 2

a = – 24Check –4(–24) + 23 + 6(–24) + 23 = –2

96 + 23 – 144 + 23 = – 2

Try this one! Don’t forget to check your work

Example –6x – 8x = 7Combine the like terms –6x and –8x first...

–14x = 7 Now, solve...

–14 –14

x =

You can check the original problem...

–6(–1/2) – 8(–1/2) = 7 3 – (– 4) 3 + 4 = 7

– 1 2

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.

6x – 2x + 10 = 46

4x + 10 = 46

4x + 10 = 46 – 10 – 10

4x = 36

x = 9

=4x4

364

Solving Multi-Step EquationsUsing the Distributive Property…

Combine like terms.

Subtract 10 from each side.

Simplify.

Divide each side by 4.

Simplify.

6x – 2(x – 5) = 46 Distributive property.

Check Your Work!

x = 9

6(9) – 2(9 – 5) = 46

Are both sides equal?

6x – 2(x – 5) = 46

6x – 2x + 11 = -5 p – 17p – 6 = -38

4x + 11 = -5

4x = -16

x = -4

-16p – 6 = -38 -16p = -32 p = 2

Extra Examples

6x – 2(x + 11) = -6

6x + (-2x) + (-22) = -6 4x + (-22) = -6

4x = 16

x = 4

Extra Examples

27 = 3c – 3(6 – 2c)

27 = 3c + (-18) + 6c

27 = 9c + (-18)

45 = 9c

5 = c

Extra Examples

PRACTICE