Solve the following equations for?. Write your answer in set notation.

a. 3x - 5 = 16

b. 3 (x + 3) - 5 = 16

c. 3 (2x - 3) - 5 = 16

d. 6 (x + 3) - 10 = 32

e. Which two equations above have the same solution set? Write a sentence explaining how the

properties of equality can be used to determine the pair without having to find the solution set for

each.

a. x=7

b. x=4

c. x=5

d. x=4

e. equation b and d have same solution set.

Step-by-step explanation:

a.

3x=21

x=21/3

x=7.

b.

3x+9-5=16

3x+4=16

3x=12

x=12/3

x=4

c.

6x-9-5=16

6x-14=16

6x=30

x=30/6

x=5

d.

6x+18-10=32

6x+8=32

6x=32-8

6x=24

x=24/6

x=4

e. Equation b and d have the same solution set.

The expression on both sides of the equal in the equation d is are twice of the expression in equation b. So, if (right side) = (left side) is true for some values of x, then 2 (right side) = 2 (left side) will be true for the same values of x. So we can find the solution without finding the solution set of both the equations.