Question

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.

Answer 1

a. x=7

b. x=4

c. x=5

d. x=4

e. equation b and d have same solution set.

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.