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) + 4 + 8x 55 – 45n or – 45n + 55

The Distributive Property, Combining Like Terms and Equations

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.

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.

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. = 30 5 5x Divide each side by 5. x = 6 Simplify.

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?

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 = 40 9j – 5 +5 +5 9j = 45 9 9 j = 5

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 35 + 10 – 5 = 40 45 – 5 = 40 40 = 40

Check Your Work You Try! z = 8 8z – 4 – 10z = – 20 Rewrite the problem. Everywhere you see a z, put in an 8 – 2z – 4 = – 20 8z - 10z - 4 = - 20 8 (8) - 10 (8) - 4 = -20 +4 = +4 64 - 80 - 4 = - 20 – 2z = – 16 – 2 – 2 - 16 - 4 = - 20 z = 8 - 20 = - 20

– 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 + 46 = – 2 – 46 –46 2a = –48 2 2 a = – 24 Check –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 = 7 Combine the like terms –6x and –8x first... –14x = 7 Now, solve... –14 –14 – 1 2 x = You can check the original problem... –6(–1/2) – 8(–1/2) = 7 3 – (– 4) 3 + 4 = 7

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.

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

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?

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

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

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

PRACTICE