Solve for the given replacement set.

Question

(A). 6y =54  {7,8,9}

(B).  2.5y=15  {0.6,6,60}

(C).  X^2 - X = 3  {1,3,9}

(D).  m - 18 = 56  {38,64,74}

Answer 1

A) The equation is 6y = 54 and replacement set is {7, 8, 9}.

When y = 7, 6(7) ≟ 54

                    42 ≠ 54

So, 7 is not a solution.

When y = 8, 6(8) ≟ 54

                    48 ≠ 54

So, 8 is not a solution.

When y = 8, 6(9) ≟ 54

                    54 = 54 True

So, 9 is a solution.

Therefore the solution set is {9}.

B) The equation is 2.5y = 15 and replacement set is {0.6, 6, 60}. 

When y = 0.6, 2.5(0.6) ≟ 15

                      1.5 ≠ 15

So, 0.6 is not a solution.

When y = 6, 2.5(6) ≟ 15

                      15 = 15 True

So, 6 is a solution.

When y = 60, 2.5(60) ≟ 15

                      1.5 ≠ 15

So, 60 is not a solution.

The solution set is {6}.

Answer 2

C) The equation is X² - X = 3 and replacement set is {1,3,9}.

When X = 1, (1)² - 1 ≟ 3

                   1 - 1 ≟ 3

                        0 ≠ 3

So, 1 is not a solution.

When X = 3, (3)² - 3 ≟ 3

                   9 - 3 ≟ 3

                        6 ≠ 3

So, 3 is not a solution.

When X = 9, (9)² - 9 ≟ 3

                   81 - 9 ≟ 3

                        72 ≠ 3

So, 9 is not a solution.

The replacement set {1,3,9} is not a solution set.

D) The equation is m - 18 = 56 and replacement set is {38, 64, 74}.

When m = 38, 38 - 18  ≟ 56

                      20 ≠ 56

So, 38 is not a solution.

When m = 64, 64 - 18  ≟ 56

                      46 ≠ 56

So, 64 is not a solution.

When m = 74, 74 - 18  ≟ 56

                      56 = 56

So, 74 is a solution.

The solution set is {74}.

Answer 3

(A). 6y =54  {7,8,9}

Divide each side by 6

y = 54/6 = 9

(B).  2.5y=15  {0.6,6,60}

divide each side by 2.5

y = 6

(D).  m - 18 = 56  {38,64,74}

add 18 to each side

m = 56 + 18 = 47