Write a two-column proof. given: 7y = 8x - 14; y = 6. prove that : x = 7.

Given: , y =6

To prove: x =7

On substituting the value of y =6 in the equation 7y = 8x -14 to solve for x.

or

42 = 8x -14                       ......[1]

Addition Property of equality states that you add the same number to both sides of an equation.

Add 14 to both sides in equation [1];

42+14 =8x -14+14

Simplify:

56 = 8x              

or

8x =56                                 ......[2]

Division Property of equality states that you divide the same number to both sides of an equation.

Divide by 8 to both sides of an equation [2];

Simplify:

x =7                             Hence proved!

A two Column proof:

 Statement                                Reason

1. 7y = 8x -14                                   Given

    y= 6

2. 7(6) = 8x -14                                Substitution property

3.  42+14 = 8x                                  Addition property of equality

4.   56 =8x                                       Simplify

5.    x =7                                           Division Property of equality

from the figure we get,

the x axis shows   the months and,

the y-axis shows the number of satisfied customer.

each line or each cell in upward direction (y-axis) shows 500.

the appropriate scale for the y - axis is: -

a = 2000 customers

b = 4000 customers

c = 6000 customers

d = 8000 customers

e = 10000 customers

f = 12000 customers

g = 14000 customers