Solving 2-Step Equations
You are trying to find the value of x that
makes this equation true (equal).


How can you do this?
-19 = -3x + 2
make both sides zero
Isolate the variable (x)
Isolate the constant 2.
How would you 
isolate the 
variable, x?

You need to isolate the variable, x, alone on one 
side of the equal sign. 
-19 = -3x + 2
 use inverse (opposite)
     operations
multiply by zero
 add x to each term
Use inverse (opposite) operations to get x alone.

Which numbers need to
be cancelled  out
to isolate the 
variable x?
-19 = -3x + 2
 Coefficient -3 & Constant -19
Constants 2 and -19
Coefficient -3 and Constant 2
The constant term
needs to
be cancelled
out first.

-3 and 2 need to be cancelled out to get x alone.
-19 = -3x + 2
Which term is the constant?
 The 2
The -3 
What would you do to BOTH sides of the equation to cancel out the constant 2?
-19 = -3x + 2
add 2
multiply 2
divide 2
subtract 2
Subtract 2 from
both sides.

What will
the equation
look like now?

-19        = -3x + 2
-  2
-17 = -3x
-21=-3x + 4
-21 = -3x
- 2
What term do you cancel next to isolate the variable x?
-21

-19        = -3x + 2
OR
-  2
-21   =   -3x
-3
- 2
What would you do
to BOTH sides of the
equation to cancel out the 
coefficient 4?
Cancel out the coefficient
-3, to isolate x.
-21   =   -3x
add -3
multiply -3
divide -3
subtract -3
What does x equal?
-21   =   -3x
-3
-3
1/7
-24
7
 -18
7 = x
-21   =   -3x
-3
-3
Substitute -3 in place of x to check your solution.
    (Will the equation be equal if -3 is the value of x?)
-19 = -3   + 2
-19 = -3        + 2
Your solution
(7)
x
-19 = -3        + 2
-19 = -3   + 2
-19 =         + 2
What is the product of -3 and 7
x
(7)
?
Since x = 7 makes the equation equal (-19=-19),
         x = 7 is the correct solution.
-19  =  -19
-19 = -21 + 2
How would you isolate the variable, p?

You need to isolate the variable, p, alone on one side of the equal sign. 
 use inverse (opposite)
     operations
multiply by zero
 add p to each term
Use inverse (opposite) operations to get p alone.

Which numbers need to
be cancelled  out
to isolate the variable p?
Coefficient -2/3 & Constant 10
 Coefficient 2/3 & Constant -10
Constants 10 and 52
The constant term 
needs to
be cancelled
out first.

The coefficient -2/3 and the constant 10 need to be cancelled out to get p alone.
Which term is the constant?
 The  10
The fraction -2/3
What would you do to BOTH sides of the equation to cancel out the constant 10?
subtract 10
multiply 10
divide 10
add 10
10      -   p = 52
Subtract 10 from
both sides.

What will
the equation
look like now?

- 10
3
2
     p - 10 = 42
     p = 42
20-   p = 62
-2 3
-2 3
23
- 10 
What term do you cancel next to isolate the variable p?
10      -   p = 52
- 10
-2/3
-   p = 42
OR
3
2
3
2
42
- 10 
What would you do
to BOTH sides of the
equation to cancel out the coefficient     ?
Cancel out the coefficient
      , to isolate p.
-2 3
-2  3
-   p = 42
2
3
multiply by the reciprocal
multiply 
add 
subtract 
23
23
23
-3
 2
What does p equal?
-3
 2 
-   p = 42
3
2
-126
-84
-63
-84
      3
-3
 2 
-3
 2 
p = -63
-   p = 42
3
2
-3
 2 
Substitute -63 in place of p to check your solution.
    (Will the equation be equal if -63 is the value of p?)
10 -           =52
10 -      = 52
23
(-63)
Your solution
23
p
10 -           =52
What is the product of 2/3 and -63
10 -        =52
10 -      = 52
23
(-63)
23
p
?
Since p =-62 makes the equation equal (52 = 52),
p = -63 is the correct solution.
10 - (-42)  =52
52 = 52
The
n
d
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