Unit 6 Review

Inequalities

100

Graph x < 7

open dot on the 7

arrow points left

200

Graph the solution

x+10 > = 12

balance the equation to get x > 2

dot on the 2

arrow points to the right

300

Solve 5x - 13 < -3

5x < 10

x < 2

400

-4x + 12 < 20

-4x < 8

x > -2 (flip the sign because the coefficient is negative)

500

-12x + 15 < -45

-12x < -60

x > 5

Distributive Property

100

7(x + 5)

7x + 35

200

12(2x - 10)

24x - 120

300

-(-3x + 10y - 7z)

3x - 10y + 7z

400

-2(3x + 7) - 2x + 5

-6x - 14 - 2x + 5

-8x - 9

500

4x + 10 - (-2x - 5)

4x + 10 + 2x + 5

6x + 15

Factoring

100

2x + 10

2(x + 5)

200

15x + 20y

5(3x + 4y)

300

-81x - 90

-9(9x + 10)

400

35x - 31x

x(35-31)

500

12xy - 8xz + 16wx

4x(3y - 2z + 4w)

Combining Like Terms

100

12x + 6x

18x

200

3x - 12 + 2x

5x - 12

300

5x + 15 - 2x - 5 + x

4x + 10

400

-6xy² + 10x - 5xy² - 2xy + 7y

10x - 11xy² - 2xy + 7y

500

6y(2x - 6) - (2y - 8)

12xy - 36y - 2y + 8 (distribute the 6y and the negative)

12xy - 38y + 8 (combine the y's)

Word problems

100

At an arcade, Sara wants a prize that's more than 100 points.  She currently has 40 points and gets 5 points for every game she wins. Write an inequality and solve for how many games does she need to win to have enough points for her prize.

40 + 5x > 100

5x > 60

x > 12

200

The temperature is 68 degrees and is rising at 2 degrees per hour.  We can go swimming if it is at least 80 degrees.  How long until we can go swimming?  

Write and solve the inequality.  What does the solution mean?

68 + 2x > = 80

2x >= 12

x >= 6

It will be (at least) 6 or more hours until it is warm enough to swim.

300

In the cafeteria, there is one large 10-seat table and many smaller 4-seat tables.  There are enough tables to fit up to 210 students.  

Write and solve an inequality for how many 4 seat tables are in the cafeteria.

10 + 4x < = 210

4x < = 200

x < = 50

400

A tub has 35 gallons of water in it and is draining at 3 gallons per hour.  How long will it take for the tub to have 2 gallons or less?

Write and solve an inequality.  What does the solution mean?

35 - 3x <= 2

-3x <= -33

x >= 11

It will take 11 or more hours to be at 2 gallons or less.

500

A rainbow fish was swimming at -5 ft.  It descended at a rate of 2 ft per minute.  How long will it take to be 20 ft below sea level or lower?

-5 - 2x <= -20

-2x <= -15

x >= 7.5 minutes