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