Combining Like Terms Unit 2, Lesson 5 Online Algebra 1

Like Terms  Like terms are terms with exactly the same variable and the same exponent on that variable.  The following are examples of like terms. Notice that they have all the same variables and same exponents: 4x and -2x -24xy 3 and xy 3 16a 2 and 11a 2  We can add and subtract like terms.  We can multiply and divide like and unlike terms.

Unlike Terms  Unlike terms do not have the same variable or the same exponent on that variable..  They cannot be added or subtracted.  Below are examples of unlike terms 5t and y -2x and 4x 3 3xy and 7x 4 y 3a and 3a 2

Combining Like terms.  To add or subtract like terms. 1. Add/subtract the coefficient, number in front of the variable. 2. Keep the variable the same. Examples: 1. 3x + 9x (3 + 9)x = 12x 2. -8x + 11x + 12 ( )x + 12 = 3x + 12

Simplify these on your own. 1. 2n – 3n 2. b – 8b v r + 8s – 19r 1. -1n or –n, remember or super hero, the invisible b v + 8, or we can say already simplified r + 8s

Solving Equations Involving Like Terms. Recall the following steps we use to solve 2-step equations: 1. If the equation involves subtraction, change the equation to addition. 2. Undo any addition, by adding the opposite to both sides. 3. Undo multiplication and division by using inverse operations. 4. Check by substituting your value in for the variable and simplifying. If you get a true statement you are correct, if not go back and check your math.

Solving Equations Involving Like Terms. In order to solve equations with like terms, we add the following step. 1. If the equation involves subtraction, change the equation to addition. 2. Combine like terms if any. 3. Undo any addition, by adding the opposite to both sides. 4. Undo multiplication and division by using inverse operations. 5. Check by substituting your value in for the variable and simplifying. If you get a true statement you are correct, if not go back and check your math. Not all steps are needed for all equations. The steps are a general guideline!

Solve: 3m + 4.5m = If the equation involves subtraction, change the equation to addition. There is none so we can skip this step. 2. Combine like terms if any. This we will use 3. Undo any addition, by adding the opposite to both sides. There is no addition so we skip this step too. 4. Undo multiplication by dividing both sides by Check by substituting your value in for the variable and simplifying. If you get a true statement you are correct, if not go back and check your math. 3m + 4.5m = m = m = 2 Check: 3(2) + 4.5(2) = = = 15

Solve 7m – 3m - 6 = 6 1. Change the subtraction to addition. 2. Combine like terms 3. Undo any addition by adding 6 to both sides. 4. Undo multiplication by dividing both sides by 4 5. Check by substituting your value in for the variable and simplifying. If you get a true statement you are correct, if not go back and check your math. 7m – 3m – 6 = 6 7m + -3m + -6 = 6 4m + -6 = m = 12 4 m = 3 Check: 7(3) – 3(3) – 6 = 6 21 – 9 – 6 = 6 12 – 6 = 6 6 = 6

Try These On Your Own! 3x -7 + x = 5 3x x = 5 4x + -7 = 5 7 4x = 12 4 x = 3 Check: 3(3) – = 5 9 – = = 5 5 = 5 x + 5x – 5 = 1 x + 5x + -5 = 1 6x + -5 = 1 5 6x = 6 6 x = 1 Check: 1 + 5(1) – 5 = – 5 = 1 6 – 5 = 1 1 = 1

Review Steps To Solving Equations.  If the equation involves subtraction, change the equation to addition.  Combine like terms if any.  Undo any addition, by adding the opposite to both sides.  Undo multiplication and division by using inverse operations.  Check by substituting your value in for the variable and simplifying. If you get a true statement you are correct, if not go back and check your math.