Basic HTML Version
Q
uantitative
R
easoning &
P
roblem
S
olving
92
© 2014 Pacific Crest
M
athematical Language
Terms and notation
literal equation
— an equation with more than one variable
isolate a variable
— to place all other variables and constants on the other side of the equation from
the isolated variable
I
nformation
What you need to know
R
eadings
M
ethodology
I
solating a
V
ariable
Scenario:
Isolate the designated variable:
x
: 6
x
– 5 = 7 + 2
x
Step
Explanation
Watch it Work!
1.
Pick a side for
the variable
Rewrite the equation and pick a side on
which to isolate the variable.
6
x
– 5 = 7 + 2
x
isolate the variable on the left side
2. Move the
constants
Move the constants to the side opposite
of where the variable will be isolated.
6
x
= 7 + 2
x +
5
3. Move all variable
terms to the
isolation side
Move the terms of the variable to be
isolated to the isolation side of the
equation.
6
x
– 2
x
= 7 + 5
4.
Combine like
terms and
simplify
Use the Distributive Property to combine
like terms on each side of the equation
and simplify.
4
x
= 12
5.
Divide by the
coefficient
Divide both sides of the equation by the
coefficient of the variable to be isolated.
4
x
= 12
x
= 3
6.
Validate
Validate that the variable has been
isolated correctly by substituting into the
original equation the computed value or
expression of the variable.
6
x
– 5 = 7 + 2
x
6(3) – 5 =
?
7 + 2(3)
18 – 5 =
?
7 + 6
13 = 13
Scenario:
Isolate the designated variable:
x
: 6
x
+ 5 –
x
= 3
x
+ 9
Step
Watch it Work!
1.
Pick a side for the variable
6
x
+ 5 –
x
= – 3
x +
9
isolate the variable on the left side
2. Move the constants
6
x
–
x
= – 3
x +
9 – 5