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© 2014 Pacific Crest
93
Step
Watch it Work!
3. Move all variable terms to
the isolation side
6
x
–
x +
3
x
=
+
9 – 5
4.
Combine like terms and
simplify
5
x
– 3
x
= 4
2
x
= 4
5.
Divide by the coefficient
2
x
= 4
x
= 2
6.
Validate
6
x
+ 5 –
x
= 3
x
+ 9
6(2) + 5 – 2 =
?
3(2) + 9
12 + 5 – 2 =
?
6 + 9
15 = 15
YOUR
TURN!
Scenario:
Isolate the designated variable:
a
: 2 4 7 2 3
a a a
a
+ = + −
M
ethodology
S
olving a
L
inear
E
quation
Scenario:
Solve the linear equation for the designated variable:
x
: 2(
x
– 3) = 4
x
– 2
Step
Explanation
Watch it Work!
1.
Choose the variable to
solve for
Note the variables and constants and
select which variable to solve for
The variable is
x.
2.
Clear parentheses
All variable occurrences should
be outside parentheses; carry out
any operations required to clear
parentheses.
2
x
– 6 = 4
x
– 2
3.
Clear fractions
Multiply both sides of the equation
by the LCD of the denominators and
simplify
No fractions
4.
Combine like terms
and simplify
Simplify the expressions on both sides
of the equation, combining like terms
whenever possible.
Simplified
5.
Isolate the variable
Rewrite so that all instances of the
chosen variable are on one side,
simplify, and rewrite the equation so
that the chosen variable is a factor.
Finally, divide by any coefficient.
Isolate the variable on the left:
2
x
– 4
x
= – 2 + 6
–2
x
= 4
x
= –2
2.4 Solving an Equation