4.3+Reasoning+with+Symbols+0809

04/08/09 AE Notes from class: F - First O - Outer I - Inner L - Last Although you can solve equations by making either tables or graphs it's more efficient to use the symbolic method.

__4.3 Reasoning with Symbols__

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

A.) 7x + 15 = 12x + 5  Method:  14-3x = 1.5x +5  14 - 3x +3 = 3 + 1.5x + 5  14 = 4.5x + 5-5  9 = 4.5x  9/4.5 = 4.5x/4.5  2 = x

B.) 14-3x = 1.5x +5 Method:  14-3x = 1.5x +5  14 - 3x +3 = 3 + 1.5x + 5  14 = 4.5x + 5-5  9 = 4.5x  9/4.5 = 4.5x/4.5  2 = x

C.) -3x + 5 = 2x - 10 Method:  -3x + 5 = 2x - 10  -3x +3 + 5 = 2x + 3 - 10  10 + 5 = 5x - 10 + 10  15 = 5x  15/5 = 5x/5  3 = x

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

E.) Check your solutions to the equations in A-D.

I checked my equations by substituting 2 for X.

In equation A, when 2 is substituted for X, both equations equal 29.

y=7x+15 y=7(2)+15 y=14+15 y=29

y=12x+5 y=12(2)+5 y=24+5 y=29

In equation B, when 2 is substituted for X, both equations equal 8.

y=14-3x y=14-3(2) y=14-6 y=8

y=1.5x+5 y=1.5(2)+5 y=3+5 y=8

In equation C, when 3 is substituted for X, both equations equal -4.

y=-3x+5 y=-3(3)+5 y=-9+5 y=-4

y=2x-10 y=2(3)-10 y=6-10 y=-4

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

y=3+5(x+2) y=3+5(7+2) y=3+5(9) y=3+45 y=48

y=7x-1 y=(7)-1 y=49-1 y=48

work well in solving linear equations.

Some strategies that helped me were to use the distributive property so that you can multiply and subtract easily when parentheses.

4.3 Follow-Up

1a.) 7.5x-23.5=51.5

”What is the value of x in the equation y=7.5x-23.5 when y=51.5?”

Method: 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

x || y || 2 || -8.5 || 4 ||  6.5 || 6 ||  21.5 || 8 ||  36.5 || 10 ||  51.5 || 1b.) 7.5x-23.5=0

”What will X be in the equation y=7.5x-23.5 when y=0?”

Method:

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

x || y || 3.10 || -0.25 || 3.11 ||  -0.175 || 3.12 ||  -0.1 || 3.13 ||  0 ||

1c.)7.5x-23.5=-30

”What will X be in the equation y=7.5x-23.5 when y=-30?”

Method:

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 that everyone in your class wrote the same expression

My expression was 4x+12=20. I don’t think that everyone wrote the same expression there are many expressions and they are very easy to make up.

4x+12=20 4x+12-12=20-12 4x=8 x=2

3a.)How many boxes must the choir sell to make a 200$ profit?

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

The boxes must sell 300 boxes to make a 200$ profit.

3b.)How many boxes must the choir sell to break even?

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

The choir must sell 100 boxes to break exactly even.