reviewing one step equations
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Reviewing One Step Equations
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Vocabulary We Need to Remember
• Term• Variable• Constant• Coefficient• Inverse Operations• PEMDAS• Combine Like Terms• Distributive Property
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One Step Equations
• Lets look back at what it means to solve an equation.
• Remember, an equation equals something, so it has the = sign.
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An Equation is like a balance scale. Everything must be
equal on both sides.
20 2x +5=
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20 2x +5=
What you do to one side of an equation, you must do to the
other side to keep it balanced!
-5-5
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15 2x =
What you do to one side of an equation, you must do to the
other side to keep it balanced!
__2
__2
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7.5 x =
What you do to one side of an equation, you must do to the
other side to keep it balanced!
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Try to solve this subtraction equation
18 n - 3=
How do you get n all by itself?
+3+3
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Try to solve this subtraction equation
21 n =
How do you get n all by itself?
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Show your check by substituting your answer back into the original
equation.
18 n - 3=
21
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Try to solve this division equation
x3 15
=
How do you get x all by itself?
•3•3
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Try to solve this division equation
x45
=
How do you get x all by itself?
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SHOW YOUR CHECK!
x3 15
=45
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to one side of an equation,When you do something
91x1
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91x1
you have to do exactlythe same thing
to the other side.
18x
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To solve an equation meansto find every number that makes the equation
true.
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In the equation,
x is the number157 x
to get 15. you add to 7
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157 xWhat is the number?
8, of course. So we would write the solution
x = 8
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In some equations, the solution is obvious.
55 x10x
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But in other equations, the solution is not so obvious.
10122 x
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10122 x
Many times we needa way to solve equations.
Especially if there is more than one step to solve.
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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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REMEMBER
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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.
Hard way Easy wayUndo Multiplication or Division 1st
Undo Addition or Subtraction 1st
3x + 4 = 16
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Hard way Easy way Undo Multiplication or Division 1st Undo Addition or
Subtraction 1st 3x + 4 = 163 3
3x3 + 4
3 = 163
- 43 - 4
3
x + 43 = 16
3
x = 123
x = 4
3x + 4 = 16 -4 -4
3x = 123 3x = 4
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1) GOAL:Get the variable on one side of the equation.
2) You always perform the same operation toboth 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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2x + 4 = 10 Get the variable alone.
- 4 - 4 Subtract 4 from both sides.
2x = 6 +4 and -4 cancel out__ __ 2 2
Divide both sides by 2 x = 3
Show your check. 2(3) +4 = 10
Finish your check.6 + 4 = 10 10 = 10
2 divided by 2 cancel to 1
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3m - 10 = 17 Get the variable alone. + 10 +10 Add 10 to both sides.
3m = 27 +10 and -10 cancel out__ __ 3 3
Divide both sides by 3 m = 9
Show your check. 3(9) – 10 = 17
Finish your check.27 – 10 = 17 17 = 17
3 divided by 3 cancel to 1
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– 4 = 8
Get the variable alone.
3 ( ) = 3 12 Multiply both sides by 3.
x = 36 3 divided by 3 cancel to 1
x 3
x 3
+4 +4 Add 4 to both sides.x 3
= 12 + 4 and -4 cancel out.
– 4 = 8 36 3
12 – 4 = 8
8 = 8
Show your check.
Finish your check.
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+ 6 = 14
Get the variable alone.
2 ( ) = 2 8 Multiply both sides by 2.
x = 16 2 divided by 2 cancel to 1
x 2
x 2
- 6 - 6 Subtract 6 from both sides.x 2
= 8 + 6 and -6 cancel out.
+ 6 = 14 16 2
8 + 6 = 14 14 = 14
Show your check.
Finish your check.
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What Operation Do You Do?
1) 3x + 8 = 24 Subtract 8
2) 5x - 10 = 19
Divide by 3FIRST SECOND
Add 10 Divide by 5
3) x - 4 = 20
2
Add 4 Multiply by 2
4) - 30 = -5x + 5 Subtract 5 Divide by -5
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3 3
1) 2x 5 19 x2) 15 63 5 5 2x 242 2x 12
15 15 x 93
x 27
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3) 8x 1 25 x4) 4 35 1 1
8x 248 8x 3
5 5
4 4 x 75
x 35
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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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The End!
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1) Undo the addition or subtraction operation first, by using inverse operations.
2) Undo the multiplication or division second, by using inverse operations.
#11
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2 Step Subtract/Multiply Equation
3m - 10 = 17 Get the variable alone. +10 +10 Add 10 to both sides.
3m = 27 +10 and -10 cancel out__ __ 3 3 Divide both sides by 3
m = 9
#12
Show your check. 3(9) – 10 =17
Finish your check.27 – 10 =17 17 =17
3 divided by 3 cancel to 1
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+ 6 = 14
Get the variable alone.
( ) = 8 Multiply both sides by 2.
x = 16 2 divided by 2 cancels out
x 2
x 2
- 6 - 6 Subtract 6 from both sides.x 2
= 8
#13
+ 6 and -6 cancel out.
+ 6 = 14 16 2
8 + 6 = 14
14 = 14
Show your check.
Finish your check.
2 2
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