Question

Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither. (5 points each) a) 2 + 3 − 6 = 10 + 4 b) 17 + 5 = 23 + 4 − 6 + c) 7 + 4 = 5 + 8 + 2 − 10

Answer 1

a) 2 + 3 - 6 = 10 + 4   ⇒   -1 = 14

This is a false statement so it has NO SOLUTIONS, which means it is a CONTRADICTION

b) 17  + 5 = 23 + 4 - 6   ⇒   25 = 21

This is a false statement so it has NO SOLUTIONS, which means it is a CONTRADICTION

c) 7 + 4 = 5 + 8 + 2 - 10   ⇒   11 = 5

This is a false statement so it so it has NO SOLUTIONS, which means it is a CONTRADICTION

NOTE: When they make a true statement, then it has infinite solutions and is an Identity