Pick a number multiply by 2 add 4 lo the product divide the

Pick a number, multiply by 2. add 4 lo the product, divide the sum by 2. and subtract two from the quotient. What relationship do you sec between the number you started with and the number you ended up with? Pick 2 more numbers. Did you get the same relationship? Explain. Can you make a conjecture about the relationship between the number you start with and the number you end with? Prove your result using algebra.

Solution

a) let the number be 2

multiplying by 2 ==> 2(2) = 4

adding four to the product ==> 4 + 4 = 8

dividing by 2 ==> 8/2 = 4

substracting by 2 ==> 4-2 = 2

we ended up with number 2

b) let the number be 3

multiplying by 2 ==> 3(2) = 6

adding four to the product ==> 6 + 4 = 10

dividing by 2 ==> 10/2 = 5

substracting by 2 ==> 5-2 = 3

we ended up with number 3

let the number be 5

multiplying by 2 ==> 5(2) = 10

adding four to the product ==> 10 + 4 = 14

dividing by 2 ==> 14/2 = 7

substracting by 2 ==> 7-2 = 5

we ended up with number 5

c) we end up with same number we choose

d) Proof by algebra

let the number be x

multiplying by 2 ==> x(2) = 2x

adding four to the product ==> 2x + 4

dividing by 2 ==> (2x + 4)/2 = x + 2

substracting by 2 ==> x + 2-2 = x

we ended up with number x