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Solving 2 Step Equations

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**Solving 2 Step Equations**

When you do something to one side of an equation,

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**Solving 2 Step Equations**

you have to do exactly the same thing to the other side.

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**Solving 2 Step Equations**

To solve an equation means to find every number that makes the equation true.

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**Solving 2 Step Equations**

In the equation, x is the number you add to 7 to get 15.

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**Solving 2 Step Equations**

What is the number? 8, of course. So we would write the solution x = 8

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**Solving 2 Step Equations**

In some equations, the solution is obvious.

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**Solving 2 Step Equations**

But in other equations, the solution is not so obvious.

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**Solving 2 Step Equations**

Many times we need a way to solve equations. Especially if there is more than one step to solve.

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**Solving 2 Step Equations**

1) Undo the addition or subtraction operation first, by using inverse operations. 2) Undo the multiplication or division operation second, by using inverse operations.

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**Solving 2 Step Equations**

REMEMBER

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**Solving 2 Step Equations**

To solve any equation, you want to get the variable all by itself. You get the variable alone by using inverse operations. Inverse Operations are like Opposites.

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**I am going to show you 2 ways to solve this equation.**

Solving 2 Step Equations I am going to show you 2 ways to solve this equation. 3x + 4 = 16 Hard way Easy way Undo Multiplication or Division 1st Undo Addition or Subtraction 1st

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**Solving 2 Step Equations**

Hard way Easy way Undo Multiplication or Division 1st Undo Addition or Subtraction 1st 3x + 4 = 16 3x + 4 = 16 3 3 3x 4 16 + = 3x = 12 3 3 3 3 3 4 16 x + = 3 3 x = 4 4 4 - - 3 3 12 x = 3 x = 4

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**Solving 2 Step Equations**

1) GOAL: Get the variable on one side of the equation. 2) You always perform the same operation to both sides of an equation. 3) To undo an operation you perform its opposite operation to both sides of the equation. 4) It is easier if you undo addition or subtraction before you undo multiplication or division.

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**Solving 2 Step Equations**

2x + 4 = 10 Get the variable alone. Subtract 4 from both sides. 2x = 6 __ __ +4 and -4 cancel out Divide both sides by 2 x = 3 2 divided by 2 cancel to 1 2(3) +4 = 10 Show your check. 6 + 4 = 10 10 = 10 Finish your check.

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**Solving 2 Step Equations**

3m - 10 = 17 Get the variable alone. Add 10 to both sides. 3m = 27 __ __ +10 and -10 cancel out Divide both sides by 3 m = 9 3 divided by 3 cancel to 1 3(9) – 10 = 17 Show your check. 27 – 10 = 17 Finish your check. 17 = 17

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**Solving 2 Step Equations**

x 3 – 4 = 8 Get the variable alone. Add 4 to both sides. x 3 = 12 + 4 and -4 cancel out. x 3 Multiply both sides by 3. 3 ( ) = 3 12 3 divided by 3 cancel to 1 x = 36 Show your check. 36 3 – 4 = 8 Finish your check. 12 – 4 = 8 8 = 8

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**Solving 2 Step Equations**

x 2 + 6 = 14 Get the variable alone. Subtract 6 from both sides. x 2 = 8 + 6 and -6 cancel out. x 2 Multiply both sides by 2. 2 ( ) = 2 8 2 divided by 2 cancel to 1 x = 16 16 2 Show your check. + 6 = 14 8 + 6 = 14 Finish your check. 14 = 14

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**Solving 2 Step Equations**

What Operation Do You Do? FIRST SECOND 1) 3x + 8 = 24 Divide by 3 Subtract 8 2) 5x - 10 = 19 Divide by 5 Add 10 3) x = 20 2 Add 4 Multiply by 2 4) - 30 = -5x + 5 Divide by -5 Subtract 5

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**Solving 2 Step Equations**

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**Solving 2 Step Equations**

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**Solving 2 Step Equations**

Think about what you need to do to isolate the variable. Get rid of addition or subtraction first. Second get rid of multiplication or division.

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**Solving 2 Step Equations**

The End! Take out your study guide!

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#11 Solve 2 Step Equations 1) Undo the addition or subtraction operation first, by using inverse operations. 2) Undo the multiplication or division second, by using inverse operations.

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**2 Step Subtract/Multiply Equation**

#12 3m - 10 = 17 Get the variable alone. Add 10 to both sides. __ __ 3m = 27 +10 and -10 cancel out Divide both sides by 3 m = 9 3 divided by 3 cancel to 1 3(9) – 10 =17 Show your check. 27 – 10 =17 Finish your check. 17 =17

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**2 Step ADD/DIVIDE Equation**

#13 2 Step ADD/DIVIDE Equation x 2 + 6 = 14 Get the variable alone. Subtract 6 from both sides. x 2 = 8 + 6 and -6 cancel out. x 2 Multiply both sides by 2. ( ) = 2 2 2 divided by 2 cancels out x = 16 16 2 Show your check. + 6 = 14 8 + 6 = 14 Finish your check. 14 = 14

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**An Equation is like a balance scale**

An Equation is like a balance scale. Everything must be equal on both sides. = 20 2x +5

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**What you do to one side of an equation, you must do to the other side to keep it balanced!**

= 20 2x +5 -5 -5

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**What you do to one side of an equation, you must do to the other side to keep it balanced!**

= 15 2x __ 2 __ 2

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**What you do to one side of an equation, you must do to the other side to keep it balanced!**

= 7.5 x

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**Try to solve this subtraction equation**

How do you get n all by itself? = 18 n - 3 +3 +3

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**Try to solve this subtraction equation**

How do you get n all by itself? = 21 n

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**Show your check by substituting your answer back into the original equation.**

= 18 21 n - 3

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**Try to solve this division equation**

How do you get x all by itself? x 3 = •3 •3 15

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**Try to solve this division equation**

How do you get x all by itself? x = 45

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