Question

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

Answer 1

Answer:

Given: $7y =8x-14$ , y =6

To prove: x =7

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

$7(6)= 8x - 14$

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];

$\frac{8x}{8} =\frac{56}{8}$

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

Answer 2

Given - 7y=8x-14 : y=6

Substitution Property - 7(6)=8x-14

Distributive Property - 8x-14=42

Addition Property - 8x=56

Division Property - x=7