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Published byEmory Anthony Modified over 3 years ago

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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)

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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.

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**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!

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**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

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**Let’s Try One… 3x + 2 = 23 - 2 -2 21 3x = 21 3 3 x = 7**

21 3x = 21 x = 7 The problem contains addition and multiplication. Which one do we undo 1st?

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**Another Example -2y – 7 = 3 +7 +7 10 -2y = 10 -2 -2 y = -5**

10 -2y = 10 y = -5 The problem contains subtraction and multiplication. Which one do we undo 1st?

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**Last Example -3c + 9 = 3 -9 -9 -6 -3c = -6 -3 -3 c = 2**

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

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**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. a = 35 Draw “the river” Subtract 3 from both sides Simplify Clear the fraction – Multiply both sides by -7 Check your answer

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**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 d = 10

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**7) Solve - 1 - 1 5 · · 5 3x = 15 3 3 x = 5 D U Draw “the river”**

· 3 ÷ 5 + 1 - 1 · 5 ÷ 3 5 · · 5 3x = 15 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

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**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

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**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

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**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.

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**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 7x = 35 x = 5

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**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. Add 6 to both sides. 7x = 14 Divide both sides by 7. x = 2 Use your calculator for the computations if needed.

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