Basic HTML Version
Q
uantitative
R
easoning &
P
roblem
S
olving
94
© 2014 Pacific Crest
Step
Explanation
Watch it Work!
6.
Validate
Substitute the solution into the original
equation to check that both sides of
the equation are the same.
(
)
?
?
?
2 – 3 4 – 2
2(( 2) 3) 4( 2) 2
2( 5) 8 2
10 10
x
x
=
− − = − −
− =− −
− = −
Scenario:
Solve the linear equation for the designated variable:
a
:
5
1
2
2 3(2 )
3
2
a a
a
− − = − −
Step
Watch it Work!
1.
Choose the variable to solve for
The variable is
a.
2.
Clear parentheses
5
1
2
2 3(2 )
3
2
5
1
2
2 6 3
3
2
a a
a
a a
a
− − = − −
− − = − −
3.
Clear fractions
LCD is 6
5
1
6 2
2 6 6 3
3
2
12 10 12 36 18 3
a a
a
a a
a
− − = − −
− − = − −
4.
Combine like terms and simplify
12
a
– 10
a
– 12 = 33 – 18
a
5.
Isolate the variable
(12 ) (10 ) 12 33 (18 )
12 10 18 33 12
20 45
45
20
9
4
a
a
a
a a a
a
a
a
− − = −
− + = +
=
=
=
6.
Validate
?
?
?
5
1
2
2 3(2 )
3
2
9 5 9
9 1
2
2 3 2
4 3 4
4 2
9 15
27 1
2 6
2 4
4 2
18 15 8 24 27 2
4 4 4 4 4 4
5 5
4 4
a a
a
− − = − −
−
− = − −
− − = − −
− − = − −
− = −