Question

Consider the equation 2x+1=16

a. Does the equation have a solution in the set of integers? ____
b. Does the equation have a solution in the set of rational numbers? ____

Answer 1

Explanation:

2x + 1 = 16

2x = 15 (subtract 1 on both sides)

x = 7.5 (divide 2 om both sides)

Since 7.5 is not an integer, (a) is No.

However 7.5 is rational, therefore (b) is Yes.

Answer 2

`2x + 1 = 16 \\ 2x = 15 \\ x =(15)/(2) \\ \boxed{x = 7.5 }`

a. Does the equation have a solution in the set of integers? ____

→As 7.5 is not a integer, the right answer is No.

b. Does the equation have a solution in the set of rational numbers? ____

→7.5 is a rational number, the right answer is Yes.