Lesson 2: Solving Equations and Inequalities Solutions.pdf · Lesson 2: Solving Equations and...
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Lesson 2: Solving Equations and Inequalities Quiz solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 1 of 5
Show all of your work in order to receive full credit.
1. Determine if x=4 is a solution of the following:
a) 6 3 21x − =
( )
?
?
?
?
6 3 21
6 4 3 21
24 3 21
21 21
Yes!
x − =
− =
− =
= �
b) 5 2 10x + >
( )
?
?
?
?
5 2 10
5 4 2 10
20 2 10
22 10
Yes!
x + >
+ >
+ >
> �
c) 30 7 2x− ≥
( )
?
?
?
?
30 7 2
30 7 4 2
30 28 2
2 2
Yes!
x− ≥
− ≥
− ≥
≥ �
Lesson 2: Solving Equations and Inequalities Quiz solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 2 of 5
2. Translate the following sentence into an equation. Then compute the solution.
Four less than twice a number is eight.
2 4 8
2 12
6
n
n
n
− =
=
=
3. Simplify the following expressions:
a) ( ) ( )4 3 8 6 27x y x y− − − +
( ) ( )4 3 8 6 27 12 32 6 27
18 5
x y x y x y x y
x y
− − − + = − + − −
= − +
b) ( )6 5 8 9
3
x + −
( )
( )
6 5 8 9 30 48 9
3 3
30 39
3
3 10 13
3
10 13
x x
x
x
x
+ − + −=
+=
+=
= +
4. Solve the following equations. Leave non-integer solutions as fractions.
a) 3 5 30x − =
3 5 30
3 35
35
3
x
x
x
− =
=
=
Lesson 2: Solving Equations and Inequalities Quiz solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 3 of 5
b) ( )52
10 2 7x= − +
( )52
352
20 352 2
552
112
10 2 7
10 5
5
5
x
x
x
x
x
= − +
= − −
+ = −
= −
− =
c) ( ) ( )2 3 5 7 8x x+ = − +
( ) ( )2 3 5 7 8
2 6 5 35 8
2 6 5 27
33 3
11
x x
x x
x x
x
x
+ = − +
+ = − +
+ = −
=
=
5. Solve the following equations for the given variable:
a) Solve for a: 2 3ak bn c+ =
2 3
2 3
2 3
2 2
3
2
ak bn c
ak c bn
ak c bn
k k
c bna
k
+ =
= −
−=
−=
Lesson 2: Solving Equations and Inequalities Quiz solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 4 of 5
b) Solve for x: ax by cx− =
( )
( )( ) ( )
( )
ax by cx
ax cx by
x a c by
x a c by
a c a c
byx
a c
− =
− =
− =
−=
− −
=−
6. Solve the following inequalities and graph the solutions on a number line:
a) 3 5 15 7x x− ≤ −
3 5 15 7
10 20
2
x x
x
x
− ≤ −
≤
≤
b) ( )11 2 4 3 26x≤ − <
( )11 2 4 3 26
11 8 6 26
3 6 18
13
2
x
x
x
x
≤ − <
≤ − <
≤ − ≤
− ≥ ≥ −
0 2
0
-1/2 -3
Lesson 2: Solving Equations and Inequalities Quiz solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 5 of 5
c) 2 3 3x − ≤ or 3 15x + >
2 3 3
2 6
3
x
x
x
− ≤
≤
≤
or 3 15
12
x
x
+ >
>
0
123 6 9