Solve 2 Step Equations Wiki
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Transcript Solve 2 Step Equations Wiki
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When you do something
to one side of an equation,
x 1 9
1
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you have to do exactly
the same thing
to the other side.
x 1 9
1 1
x 8
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To solve an equation means
to find every number that
makes the equation true.
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In the equation,
x 7 15
x is the number
you add to 7
to get 15.
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What is the number?
x 7 15
8, of course.
So we would write the solution
x=8
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In some equations,
the solution is obvious.
x 5 5
x 10
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But in other equations,
the solution is not so obvious.
2x 12 10
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Many times we need
a way to solve equations.
2x 12 10
Especially if there is more
than one step to solve.
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the addition or
subtraction operation first,
by using inverse operations.
2) Undo the multiplication or
division operation second,
by using inverse operations.
1) Undo
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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.
3x + 4 = 16
Hard way
Easy way
Undo Multiplication
or Division 1st
Undo Addition or
Subtraction 1st
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Hard way
Easy way
Undo Multiplication or Division 1st
Undo Addition or Subtraction 1st
3x + 4 = 16
3
3
3x + 4 = 16
3
3
3
x + 4 = 16
3
3
- 4 - 4
3
3
x = 12
3
x = 4
3x + 4 = 16
-4 -4
3x = 12
3
3
x=4
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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
inverse 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
-4 -4
2x = __
__
6
2
2
x
=3
2(3) +4 = 10
6 + 4 = 10
10 = 10
Get the variable alone.
Subtract 4 from both sides.
+4 and -4 cancel out
Divide both sides by 2
2 divided by 2 divides to 1
Show your check.
Finish your check.
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3m - 10 = 17
+ 10 +10
3m
__
3
m
= __
27
3
=9
3(9) – 10 = 17
27 – 10 = 17
17 = 17
Get the variable alone.
Add 10 to both sides.
+10 and -10 cancel out
Divide both sides by 3
3 divided by 3 divides to 1
Show your check.
Finish your check.
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x
3
3
x
3
x
(3
x
36
3
–4=8
+4 +4
Get the variable alone.
= 12
+ 4 and -4 cancel out.
Add 4 to both sides.
) = 3 12 Multiply both sides by 3.
= 36
–4=8
12 – 4 = 8
8=8
3 divided by 3 divides to 1
Show your check.
Finish your check.
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x
2
2
x
2
x
(2
x
16
2
+ 6 = 14
-6 -6
Get the variable alone.
Subtract 6 from both sides.
+ 6 and -6 cancel out.
=8
) =2 8
Multiply both sides by 2.
= 16
2 divided by 2 divides to 1
+ 6 = 14
8 + 6 = 14
14 = 14
Show your check.
Finish your check.
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What Operation Do You Do?
1) 3x + 8 = 24
FIRST
Subtract 8
SECOND
Divide by 3
2) 5x - 10 = 19
Add 10
Divide by 5
3) x - 4 = 20
2
Add 4
Multiply by 2
4) - 30 = -5x + 5 Subtract 5
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Divide by -5
1) 2x 5 19
5 5
2x 24
2
2
x 12
x
2) 15 6
3
15
15
x
3 3 9 3
x 27
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3) 8x 1 25
1 1
8x 24
8 8
x3
x
4) 4 3
5
4 4
x
5 5 7 5
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!
Take out your study guide!
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#11
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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#12
2 Step Subtract/Multiply Equation
3m - 10 = 17
+10 +10
__
3m
3
m
__
= 27
3
=9
3(9) – 10 =17
27 – 10 =17
17 =17
Get the variable alone.
Add 10 to both sides.
+10 and -10 cancel out
Divide both sides by 3
3 divided by 3 cancel to 1
Show your check.
Finish your check.
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#13
x
2
x
2
x
2( 2
x
+ 6 = 14
-6 -6
=8
Get the variable alone.
Subtract 6 from both sides.
+ 6 and -6 cancel out.
) = 2 8 Multiply both sides by 2.
= 16
16
+
6
=
14
2
8 + 6 = 14
14 = 14
2 divided by 2 cancels out
Show your check.
Finish your check.
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TEACHER NOTE: Use the
following slides the next day
when correcting homework.
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HOMEWORK
EXPLANATION
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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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What you do to one side of an
equation, you must do to the
other side to keep it balanced!
=
20
-5
2x +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
__
2
2x
__
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
+3
n -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
=
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15 •3
Try to solve this division equation
How do you get x all by itself?
x
=
45
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SHOW YOUR CHECK!
45
x
3
=
15
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