Using the equation below, identify the following vocabulary terms. 4x + 3 = 15 1.) Coefficient 2.) Variable 3.) Constant 4.) Like Terms 5.) Is this a one or two step equation? 4 x 3 and 15 Two step

LESSON 6 DISTRIBUTIVE PROPERTY

 Your scale/equation must stay balanced. Whatever you do on one side, you must do the same thing on the other.  Start by combining like terms on each side of the equal sign.  Make sure to get all of the variables on one side and all of the constants on the other.  Remember to check your work.

Let’s review the distributive property. The addition of two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses, such as a(b + c) = ab + ac. So what does this mean?

This means, that if you have 3(4 + 2) You can do either of the following. 3(4 + 2) = 3(6) = 18 OR 3(4) + 3(2) = = 18 So, let’s try the distributive property with a variable…

2 (x + 3) = 10 What’s our first step? Let’s use the distributive property. What will the new equation look like when we distribute the 2? 2x + 6 = 10 - This we can solve. - 6 = - 6 2x = 4 Divide both sides by 2 x = 2 2 (2 + 3) = 10 2 (5) = = 10

2 (x + 3) = 9 + x 2x + 6 = 9 + x Now get everything with a variable to one side of the equal sign and everything without a variable to the other side. 2x + 6 = 9 + x - 6 = - 6 2x = 3 + x - x - x 2 (3 + 3) = (6) = = 12 x = 3

2(2x + 1) = 3x + 8 4x + 2 = 3x x = -3x x + 2 = 8 -2 = -2 x = 6 And of course, don’t forget to check your work!

2(2x + 3) = x +9 4x + 6 = x +9 x = 1

The first two teams to name 5 items in the following category will win their choice of a Spartan Buck or Tootsie Rolls. Name 5 animals that start with the letter P.

2(2x + 2) = 20 4x + 4 = 20 x = 4

x + 6 = 2x = x = 2(5) = = 11

x + 2x + x + x + 3 = 8 Start by combining like terms. 5x + 3 = 8 x = 1

3(x + 1) + 2 = 2(x + 5) 3x = 2x + 10 Can you combine any like terms? x = 5 Let’s check the work. 3(5+1) + 2 = 2(5+5) 3(6) + 2 = 2(10) = = 20

3x + 3 = x + 21 Subtract x from each side. 2x + 3 = 21 Subtract 3 from each side. 2x = 18 Divide each side by 2 x = 9 CHECK YOUR WORK!

2x x = x + 8 4x + 2 = x + 8 x = 2

Let’s look at the scale for the current learning goal in your folder. We’re approximately halfway through this goal, so it’s time to track your progress again. Mark your current level in the middle section at the bottom and put today’s date.

The following problem has an incorrect step. Using complete thought sentences, tell which step is incorrect and what should have been done. 4x + 2x + 3 = x x + 3 = x x + 3 = x x -x 2x + 3 = x = 12 ÷ 2 ÷ 2 x = 6