Solving Equations With Variables On Both Sides!

Simplifying Expressions

100

3x + 2 - x + 4

2x + 6

200

-3x + 4y - 2y + 5x - 10

2x +2y -10

300

10xy - x + 7y + 3x - 12y

10xy + 2x - 5y

400

6xy + 2xz - 4xy + 5x - 7xz

2xy - 5xz + 5x

500

Which equations are equivalent to: 5x + 1 - (2x-8)

a) 5x + 1 - 2x - 8

b) 5x + 1 - 2x + 8

c) 3x + 9

d) 5x + (-2x) + 1 + 8

Answer: B, C, D

Factoring/Distributive Property (MUST BE SIMPLEST FORM)

100

2(3x+8)

6x+16

200

-2x + 8

-2(x-4)

300

2(x-8) + 3(x-2)

2x-16+3x-6

5x-22

400

-1/2(x - 10) + 2(x + 6)

-1/2x + 5 + 2x + 12

1.5x+17

500

Write the following in one simple factored form. 

(2-x)3 - 5(x - 2)

6-3x - 5x + 10

-8x+16  (+250 if correct til here)

-8(x-2)   (+500 if completed)

All, Some or No Solutions(Solve if One Solution)

100

2x + 3x - 10 = 5x - 8 - 2

All Solutions

200

5x - 2 = 3x - 2

One Solution

x=0

300

2x - 6 + 8 = 2(x+9)

No Solution 

400

10x - 8 = 2(x+16)

One Solution

x=5

500

4xy - 2(xy - 8) = 8 - 5xy + 7xy

All Solutions

Solve Variables on Both Sides

100

5n + 9 = 2n + 12

n = 1

200

8y - 3 = 6y + 17

y = 10

300

6x + 5 - 2x = 3x + 26

x = 21

400

3x - 4 + 2x + 2 = 3x + 1

x = 3/2

500

10x + 5 = -5(4x - 7)

x=1

Word Problems

100

On a beach trip, Lucy rents a bike from “Wheels by the Waves”, where they rent bikes for $12 plus $3 per hour. If Lucy spent $30, how many hours (h) did she rent a bike?

6 hours

200

James bought a cheeseburger, fries and a drink for dinner. The cheeseburger was three times the price of the fries, and the drink and the fries were the same price. If the entire meal cost $12.50, what was the price of the cheeseburger?

$7.50

300

Company A's bounce house rental is $30 to set up, and $10 per hour it is rented.

Company B's bounce house rental is $60 to set up, and $5 per hour it is rented.

At what hour will the companies be the same cost to rent? 

30+10x = 60 + 5x

x=6 hours

400

While at the beach, Daniel buys lunch for his family from a food stand. He purchases one hot dog for $2.50 and 3 hamburgers. If he spent less than $13 total, write and solve an inequality to find h, the possible amount each hamburger could cost.

2.50 + 3x < $13

h < $3.50

500

The water temperature at a public pool started at 82 degrees, and it is decreasing 3 degrees each hour as it gets colder. 

If the water temperature needs to be warmer than 70 degrees, write and solve an inequality to find h, the number of hours that can go by until the pool must be closed for the evening. 

t=82-3h

70 < 82 - 3h

-12 < -3h

4 > h   (Hours must be less than 4)