Equations and Inequalities..

Please show all steps of your solution must be shown and a few words to explain what you did to solve the problem. For instance, if lowest common denominators are required show how you determined the value of the LCD. If factors are removed, show the value of the total factor removed. Please do not just supply an answer.

1.      Solve the following equation
                  -1/2 + 3y = 4y             
 
2.      Solve the following equation
                  -(3/4)z - (2/3) = 1/3    
 
3.      State the solution set in interval notation and sketch the graph
 3 <= x <= 7
 
4.      At Burger Brothers the price of a hamburger is twice the price of an order of  french fries, and the price of a Pepsi is $0.40 more than the price of the fries.  Burger Brothers advertises that you can get a complete meal (burger, fries, and Pepsi ) for under $4.00. What is the price range of an order of fries?
 

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...ide

-1/2 + 3y - 3y = 4y - 3y

-1/2 = y

OR

y = -1/2

2. Solve the following equation
-(3/4)z - (2/3) = 1/3

Multiply whole equation by 12 as LCD of 4 and 3 is 12(they don't have any factor in common).

-12*(3/4)z -(2/3)*12 = (1/3)*12

-9z - 8 = 4

Add 8 to each side, we will have

-9z - 8 + 8 = 4 + 8

-9z = 12

Divide each side by -9, we will have

z = ...