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Solving Steps
Using Distribution
Combining Like Terms
Mash Up!
Dependent vs Independent
100

Simplify the following:

4(x + z) + 8

4x + 4z + 8

100

2(x - 7) = 10

x = 12

100

6 + 10x - 4x -x = 1

x = -1

100

-7y + 12 - 2y = - 6

y = 2

100

Tristan picks a marble at random. Without putting the first marble back, he picks another marble at random. Are the two event dependent or independent?

Dependent

200

Simplify the following:

2z + 5z - 3y + y

7z - 2y

200

5(x + 2) = -20

x = -2

200

-7x - 10 = -8x - 4x

x = 2

200

2(x - 8) + 10x - 7x =  39

x = 11

200

Students in a composition class may select certain topics on which to write an essay. Repeats are allowed, and they do not need to inform the teacher of their choice prior to the due date of the essay. Are these two events dependent or independent?

Independent

300

Simplify the following:

6(2a - 3b) + 2(-4b + 2) -3

12a - 26b + 1

300

3(2 + x) -5x = 16

x = -5

300

10 = -2x + 4x + 8x

x = 1

300

-3(v + 4) - 2v = - 37

v = 25

300

Riley calls a bakery and orders a custom cake with a certain design. Later that day, Josiah calls to order a custom cake.

Are these two events dependent or independent?

Independent

400

Simplify the following:

7y3 + 8(3y - 4y2) + 2x2

24y - 30y2 + 7y3

400

-152 = 4x - 4(6x + 13)

x = 5

400

13 + 4x + 3x - 3x = 1

x = -3

400

17 = 4(n + 11) + 5n

n = -3

400

Annie and Simon get haircuts from the same stylist. Annie calls before lunch to book one of the open appointment times. After lunch, Simon calls and chooses from among the remaining appointments.

Are these two events dependent or independent?

Dependent 

500

Simplify the following:

2(4 + 2x) + 3x3

3x3 + 4x + 8

500

5x + 2(1 - x) -4x = - 2

x = 4

500

-5 + 7 + 8 = 2x + 3x

x = 5

500

3 = 6b + 5 - 5b

b = -2

500

A third grade teacher is assigning parts for the class play. Bryant's role will be selected first, and Peter will be assigned a role next.

Are these two events dependent or independent?

Dependent