Equations & Inequalities (U1 - P2)

Justify(DO IN ORDER)

100

Given: -7 + 2x + 1 = -8x - 2(7 - 3x)

Step 1: -7 + 2x + 1 = -8x - 14 + 6x  (Property: ?????)    

Distributive Property

200

Given: -7 + 2x + 1 = -8x - 2(7 - 3x)

Step 1: -7 + 2x + 1 = -8x - 14 + 6x

Step 2: 2x - 6 = -2x - 14   (Property: ?????)

Combine like terms

300

Given: -7 + 2x + 1 = -8x - 2(7 - 3x)

Step 1: -7 + 2x + 1 = -8x - 14 + 6x

Step 2: 2x - 6 = -2x - 14 

Step 3: 4x - 6 = -14     (Property: ?????)

Addition property of =

400

Given: -7 + 2x + 1 = -8x - 2(7 - 3x)

Step 1: -7 + 2x + 1 = -8x - 14 + 6x

Step 2: 2x - 6 = -2x - 14 

Step 3: 4x - 6 = -14

Step 4: 4x = -8     (Property: ?????)

Addition property of =

500

Given: -7 + 2x + 1 = -8x - 2(7 - 3x)

Step 1: -7 + 2x + 1 = -8x - 14 + 6x

Step 2: 2x - 6 = -2x - 14 

Step 3: 4x - 6 = -14

Step 4: 4x = -8

Step 5:  x = -2     (Property: ?????)

Division property of =

Literal Equations

100

Solve for b:

A = (a + b)/2

b = 2A - a

200

Solve for r:

I = prt

r = I/(pt)

300

Solve for h:

S = 2pirh

h = S/(2pir)

400

Solve for y:

ax + by + c = 0

y = (-ax - c)/b

500

Solve for x:

P = (144x)/y

x = (Py)/144

Solve Inequalities

100

-3x - 12 <= -9

x >= -1

200

Solve:

-3(k - 9) > 3k + 3

k < 4

300

Solve:

2(y + 6) <= 3y

y >= 12

400

Solve and graph:

2x - 4 < 2(3x - 1)

x > -1/2

500

Solve and graph:

7(x + 3) <= 4(x - 6)

 

x<= -15

Solve word problems(DO IN ORDER)

100

Write an inequality:

You start with $52 in your savings account and deposit $27 each week. You want to buy a bicycle that costs $340. Write an inequality to represent the least number of weeks you can work to purchase the bike.  

x = # of weeks

52 + 27x >= 340

200

Using the information from the 100 question:

(You should solve the previous problem.)

If you do this for 11 weeks, will you have enough to buy a bicycle that costs $340? Why?

Yes, because you would need to work for more than approximately 10.7 weeks.

300

Write an inequality:

Stephanie is saving money to buy a computer next year. So far she has saved $200. Write an inequality to show how much she needs to save each month for the next year so she has at least $1200 to spend on the computer.

200 + 12x >= 1200

400

Using the information from the 300 question, solve.

x >= 83.33

500

Caleb is saving money to buy a bike. So far he has saved $150. Write an inequality to show how much he needs to save for the next 10 months to have at least $800 to spend on the bike.

1) Identify the variable.

2) Write the inequality.

3) Solve.

1)  x = $

2 & 3)  

150 + 10x >= 800

x >= 65