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One-Step Equations
Using Opposite Operations
When working to get the variable
isolated and all alone, use the
opposites rule.
Opposites Rule – to get rid of a
term from either side of an
equation, just do the opposite
operation.
To ISOLATE a variable, simply add
or subtract to get the variable all
alone.
To get rid of a term that is……..
…connected to its side by
addition, subtract it from
both sides.
To get rid of a term that is……..
…connected to its side by
subtraction, add it to both
sides.
Variable
Mark the variable then leave
it alone. Move everything
away from the variable.
C
Variable
1. C + 3 = 5
-3 -3
= 2
2. m - 3 = 5
+3 +3
m = 8
“fix” double signs first
3. P + (-12) = -5
P – 12 = -5
+12 +12
P
=7
“fix” double signs first
4. Y - (-6) = 3
Y+6=3
- 6 -6
Y
= -3
5. X + 2.2 = 9.2
- 2.2 - 2.2
X
=7
6. X – (-28) = - 48
X + 28 = - 48
- 28 - 28
X = - 76
Once you have isolated the
variable, you are ready to SOLVE.
Multiply or Divide to solve for the
variable.
To get rid of a term that is………
… connected by multiplication,
divide both sides by the number in
front of the variable.
… connected by division, multiply
both sides by the number in front
of the variable. (the denominator)
7. 9x = 45
9
9
x =5
8. - 4m = - 28
-4
-4
m=7
This reads 9 times x
So use the opposite.
Divide both sides by 9.
k
(8)
(8)
9.
6
8
Now
Divide
By -1
- k = 48
-1
-1
k = - 48
(-5)
10.
x (-5)
11 
5
55 = x
3 m

4 12
11.
36 = 4m
4
4
9
= m
12.(3)
2n
(3)
 12
3
2n = 36
2
2
n = 18
3
13. 5 x  2
4
(4)
-5x =
11
4
(4)
-20x = 11
-20
-20
-11
X =
20
First, change this to
an improper fraction.
(5)
14. 50 
3(5)
y
5
-250 = -3y
-3
-3
83.333 = y
1
83
3
= y
6.4  0.8x
4
2
x  9
5
35