Download Solving 2 Step Equations

Reviewing One Step
Equations
http://www.mathslideshows.com
Vocabulary We Need to
Remember
•
•
•
•
•
•
•
•
Term
Variable
Constant
Coefficient
Inverse Operations
PEMDAS
Combine Like Terms
Distributive Property
http://www.mathslideshows.com
One Step Equations
• Lets look back at what it means to solve an
equation.
• Remember, an equation equals something,
so it has the = sign.
http://www.mathslideshows.com
An Equation is like a balance
scale. Everything must be
equal on both sides.
=
20
2x +5
http://www.mathslideshows.com
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
http://www.mathslideshows.com
What you do to one side of an
equation, you must do to the
other side to keep it balanced!
=
15
__
2
2x
__
2
http://www.mathslideshows.com
What you do to one side of an
equation, you must do to the
other side to keep it balanced!
=
7.5
x
http://www.mathslideshows.com
Try to solve this subtraction equation
How do you get n all by itself?
=
18
+3
n -3
+3
http://www.mathslideshows.com
Try to solve this subtraction equation
How do you get n all by itself?
=
21
n
http://www.mathslideshows.com
Show your check by substituting your
answer back into the original
equation.
=
18
21
n -3
http://www.mathslideshows.com
Try to solve this division equation
How do you get x all by itself?
x •3
3
=
http://www.mathslideshows.com
15 •3
Try to solve this division equation
How do you get x all by itself?
x
=
45
http://www.mathslideshows.com
SHOW YOUR CHECK!
45
x
3
=
15
http://www.mathslideshows.com
http://www.mathslideshows.com
When you do something
to one side of an equation,
x 1  9
1
http://www.mathslideshows.com
you have to do exactly
the same thing
to the other side.
x 1  9
1 1
x 8
http://www.mathslideshows.com
To solve an equation means
to find every number that
makes the equation true.
http://www.mathslideshows.com
In the equation,
x  7  15
x is the number
you add to 7
to get 15.
http://www.mathslideshows.com
What is the number?
x  7  15
8, of course.
So we would write the solution
x=8
http://www.mathslideshows.com
In some equations,
the solution is obvious.
x 5  5
x  10
http://www.mathslideshows.com
But in other equations,
the solution is not so obvious.
2x  12  10
http://www.mathslideshows.com
Many times we need
a way to solve equations.
2x  12  10
Especially if there is more
than one step to solve.
http://www.mathslideshows.com
the addition or
subtraction operation first,
by using inverse operations.
2) Undo the multiplication or
division operation second,
by using inverse operations.
1) Undo
http://www.mathslideshows.com
REMEMBER
http://www.mathslideshows.com
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.
http://www.mathslideshows.com
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
http://www.mathslideshows.com
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
http://www.mathslideshows.com
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.
http://www.mathslideshows.com
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 cancel to 1
Show your check.
Finish your check.
http://www.mathslideshows.com
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.
http://www.mathslideshows.com
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 cancel to 1
Show your check.
Finish your check.
http://www.mathslideshows.com
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 cancel to 1
+ 6 = 14
8 + 6 = 14
14 = 14
Show your check.
Finish your check.
http://www.mathslideshows.com
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
http://www.mathslideshows.com
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
http://www.mathslideshows.com
3) 8x  1  25
1  1
8x  24
8 8
x3
x
4)  4  3
5
4  4
x
 5 5  7  5 
x  35
http://www.mathslideshows.com
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.
http://www.mathslideshows.com
The End!
http://www.mathslideshows.com
#11
1) Undo the addition or subtraction
operation first, by using inverse
operations.
2) Undo the multiplication or
division second, by using inverse
operations.
http://www.mathslideshows.com
#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.
http://www.mathslideshows.com
#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.
http://www.mathslideshows.com