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Q
uantitative
R
easoning &
P
roblem
S
olving
100
© 2014 Pacific Crest
D
emonstrate Your Understanding
Apply it and show you know in context!
Solve each equation for the indicated variable.
1. Solve for
a
: 2
a
+ 3 = 7 – 3(2 – 5
a
)
2. Solve for
x
: 5(
x
– 3) + 4 = –7 + 3
x
3. Solve for
x
:
3
5
2( 5)
4
4
3
x
x
x
− − + = −
4. Solve for
r
: 5 – 3
a
+ 4 = 3 – 2(
a
+
r
) – 7
5. Solve for
y
: 2(
x
– 3) = 5 – 3
x
+
y
+ 5
x
6. Solve for
t
: 2
x
– 5
t
= 3(
t
– 4) + 7
H
ardest Problem
How hard
can
it be? Can you still use what you’ve learned?
Based on the Model, the Methodology, and the Demonstrate Your Understanding (DYU) problems in
this activity, create the
hardest
problem you can. Start with the hardest DYU problem in this experience
and by contrasting and comparing it with the other DYU problems, play “What if” with the different
conditions and parameters in the various problems.
Can you still solve the problem? If so, solve it. If not, explain why not. What is it that makes a problem
where you solve an equation a difficult problem to solve?
What are the conditions and parameters that make a problem involving solving an equation a difficult
problem to solve?
T
roubleshooting
Find the error and correct it!
Brandon finally felt comfortable solving equations; it was following the methodology and learning
that process that seemed to help. But when he got his homework back, he noticed that his instructor
had marked problem 4 as “completely incorrect” (there was even some red ink involved!). Brandon
opened his book to the pertinent metho-dology and traced through his work. He was SURE he’d
followed it correctly. Where did he go wrong?
Identify the error and provide a correction.
4. Solve for
t
:
2
3 4 5 6 5 4( 3 )
s t
s s s
t
− + + = − − + −
Brandon’s solution
−
= − −
−
= − − −
= − −
= −
− −
= − −
−
= − −
= − −
2
3 + 4 + 5 6 5 4( + 3 )
9 + 4 + 5 6 5 4 12 + 4
9 + 4 + 5 3 12 + 4
4 + 3 12 + 4 9 5
7 12 9 + 4 5
7 21
3
7
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
t
t
t
t
t
t
t
t
t
t
t
t