4.3+Reasoning+with+Symbols+0910

May 8, 2010**
 * AS
 * Big Idea:** Equations can be used to model real things.
 * Essential Question:** How do I create and solve equations?


 * Problem 4.3- Reasoning with Symbols**


 * In A-D, use the symbolic method to solve the equation.**

7x + 15 = 12x + 5 7x + 15 - 5 = 12x + 5 - 5 7x + 10 = 12x 7x + 10 - 7x = 12x - 7x 10 = 5x 10/5 = 5x/5 2 = x x = 2
 * A. 7x + 15 = 12x + 5**

14-3x = 1.5x +5 14 - 3x +3x = 3x + 1.5x + 5 14-5 = 4.5x + 5-5 9 = 4.5x 9/4.5 = 4.5x/4.5 2 = x x = 2
 * B. 14 - 3x = 1.5x + 5**

**C. -3x + 5 = 2x - 10** -3x + 5 = 2x - 10 -3x +3x + 5 = 2x + 3x - 10 5=5x-10 5+ 10 = 5x - 10 + 10 15 = 5x 15/5 = 5x/5 3 = x x=3

3 + 5(x+2) = 7x - 1 3 + 5x + 10 = 7x -1 5x + 13 = 7x -1 5x + 13- 5x= 7x -1- 5 x 13 = 2x - 1 13 + 1= 2x -1 + 1 14 = 2x 14/2 = 2x/2 7 = x x = 2
 * D. 3 + 5(x+2) = 7x – 1**

In equation A, when 2 is substituted for X, both equations equal 29.
 * E.** **Check Your solutions to the equations in a-d.**

7x + 15 = 12x + 5 7(2)+ 15= 12(2) + 5 14+ 15= 24+5 29=29 In equation B, when 2 is substituted for X, both equations equal 8.

14-3x = 1.5x +5 14- 3(2)= 1.5(2) + 5 14- 6=3+5 8=8 In equation C, when 3 is substituted for X, both equations equal -4.

-3x + 5 = 2x - 10 -3(3)+ 5= 2(3) - 10 -9 + 5 = 6 -10 -4 = -4

In equation D, when 7 is substituted for X, both equations equal 48.

3 + 5(x+2) = 7x - 1 3 + 5(7+ 2) = 7(7) -1 3 + 35+ 10 = 49-1 48=48


 * F. Look over your work for A-D. Record any general strategies that seem to work well in solving linear equations.**

__**Problem 4.3 Follow-Up**__
 * Try to get the variables on one side and the non-variables on the other side
 * What you do to one side, you do it to the other
 * Try to make x by itself
 * Start with doing the things in the parenthesis, then do the addition and subtraction, and then end with the division


 * 1. In a-c, the given equation is related to the equation y= 7.5x -23.5. Explain what question the solution to the given equation answers. For example, the solution to 7.5x -23.5= 10 answers the question "what is the value of x in the equation y= 7.5 x - 23.5 when y= 10?" Then use a table or a graph to solve the equation, and explain how you found your solution.**

7.5x-23.5=51.5 7.5x-23.5+23.5=51.5+23.5 7.5x=75 7.5x/7.5 = 75/7.5 x=10
 * 1a. 7.5x- 23.5 = 51.5**
 * x || y ||
 * 2 || -8.5 ||
 * 4 || 6.5 ||
 * 6 || 21.5 ||
 * 8 || 36.5 ||
 * 10 || 51.5 ||

7.5x-23.5=0 7.5x-23.5+23.5=0+23.5 7.5x=23.5 7.5x/7.5=23.5/7.5 x=3.1333333
 * 1b. 7.5x - 23.5=0**
 * x || y ||
 * 3.10 || -0.25 ||
 * 3.11 || -0.175 ||
 * 3.12 || -0.1 ||
 * 3.13 || 0 ||


 * 1c. 7.5x - 23.5=-30**

7.5x-23.5=-30 7.5x-23.5+23.5=-30+23.5 7.5x=6.5 7.5x/7.5=6.5/7.5 x=0.8666666
 * x || y ||
 * -1 || -31 ||
 * -0.9 || -30.25 ||
 * -0.866 || -30 ||
 * -0.8 || -29.5 ||
 * -0.7 || -28.75 ||


 * 2. Write a linear equation with a solution of x = 2. Do you think everybody in your class wrote the same equation?**

51=25x+1 51=25(2)+1 51=50+1 51=51

I don't think that everybody in the class wrote the same equation. The equation depends on what you choose for the variable y.

P=3x-(100+2x)
 * 3.** **The school choir is selling boxes of greeting cards to raise money for a trip. The equation for the profit in dollars, P, in terms of the number of boxes sold, x, is

3a. How many boxes must the choir sell to make a $200 profit? Explain how you found your answer.**

200=3x-(100+2x) 200=3x-2x-100 200=x-100 200+100=x-100+100 300=x x=300

The choir needs to sell 300 boxes.


 * 3b. How many boxes must the choir sell to break even? Expain how you found your answer.**

0=3x-(100+2x) 0=3x-2x-100 0=x-100 0+100=x-100+100 100=x x=100