Rules to Remember When solving an equation, the goal is to get the variable by itself. Addition and Subtraction are inverse operations. (opposites) Multiplication and Division are inverse operations. (opposites)

Don’t Forget The equation is like a balance scale. Whatever you do to one side of the equation must be done to the other side of the equation.

How to solve two-step equations “Undo” the operations in the reverse order of the order of operations. You are using the work back-words strategy In order of operations we do multiplication or division first, then addition and subtraction. When solving an equation we do the opposite!

Integer Rules to Remember Adding Integers Same sign= add and keep the sign Different sign = subtract and keep the sign of the larger number Subtracting Integers Keep, Change, Change Follow the rules for addition Multiplying and Dividing Integers Same Sign = Positive Answer Different Sign = Negative Answer

Let’s Try One… 3x + 2 = 23 - 2 -2 21 3x = 21 3 3 x = 7 - 2 -2 21 3x = 21 3 3 x = 7 The problem contains addition and multiplication. Which one do we undo 1st?

Another Example -2y – 7 = 3 +7 +7 10 -2y = 10 -2 -2 y = -5 +7 +7 10 -2y = 10 -2 -2 y = -5 The problem contains subtraction and multiplication. Which one do we undo 1st?

Last Example -3c + 9 = 3 -9 -9 -6 -3c = -6 -3 -3 c = 2 -9 -9 -6 -3c = -6 -3 -3 c = 2 The problem contains addition and multiplication. Which one do we undo 1st?

5) Solve -3 -3 a = 35 D U Draw “the river” Subtract 3 from both sides ÷ -7 + 3 - 3 · -7 Do/Undo Chart – This one is tricky! Remember to always use the sign in front of the number. -3 -3 a = 35 Draw “the river” Subtract 3 from both sides Simplify Clear the fraction – Multiply both sides by -7 Check your answer

3) Solve d = 10 d – 4 = 6 + 4 + 4 D U Draw “the river” - 4 ÷ 2 · 2 + 4 Draw “the river” Clear the fraction - Multiply both sides by 2 Simplify Add 4 to both sides Check your answer d – 4 = 6 + 4 + 4 d = 10

7) Solve - 1 - 1 5 · · 5 3x = 15 3 3 x = 5 D U Draw “the river” · 3 ÷ 5 + 1 - 1 · 5 ÷ 3 - 1 - 1 5 · · 5 3x = 15 3 3 x = 5 Draw “the river” Subtract 1 from both sides Simplify Clear the fraction -Multiply both sides by 5 Divide both sides by 3 Check your answer

REVIEW: Simplify Using the Distributive Property. Distributive Property – Multiply times everything in the parentheses. a ( b + c ) = ab + ac OR a ( b – c ) = ab – ac Example 1: -3 ( x + 5 ) -3x – 15 Example 2: -7 ( 2a – 4 ) -14a + 28

REVIEW: Simplify Using Combining Like Terms Like Terms must have the same variables and the same powers on the letters. Combine like terms by adding or subtracting the coefficients (numbers in front of the variables). Example 1: 3x + 5 – 7x + 9 -4x + 14 Example 2: 3 – 6y – 7 – 9y -4 – 15y

How do we simplify and solve equations with multiple steps? To solve equations with multiple steps, first use the distributive property to get rid of the parentheses. Then, combine like terms to get the problem in the 2-step form. Solve by using inverse operations as you do with 2-step equations.

Simplify and Solve Example: 3x + 2 ( 2x – 1 ) = 33 Use Distributive Property 2. Combine Like terms 3. Use Inverse Operations 3x + = 33 4x – 2 7x – 2 = 33 + 2 + 2 7x = 35 7 7 x = 5

Simplify and Solve Equations FIRST - Use the Distributive Property to get rid of the parentheses. Example: 3 ( x – 2 ) + 4x = 8 SECOND: Combine like terms. 3x – 6 + 4x = 8 Copy the rest of the problem. 7x – 6 = 8 Now it’s a regular 2-step equation. + 6 + 6 Add 6 to both sides. 7x = 14 Divide both sides by 7. 7 7 x = 2 Use your calculator for the computations if needed.