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) 2x + 3x − 6 = 10 + 4x b) 17 + 5x = 23 + 4x − 6 + x c) 7x + 4 = 5x + 8 + 2x − 10

Answer 1

a)

2x + 3x - 6 = 10 + 4x

5x - 4x = 16

x = 16 Neither One solution.

b) 17 + 5x = 23 + 4x - 6 + x

5x + 17 = 5x + 17

This is an identity with infinite solutions.

c) 7x + 4 = 5x + 8 + 2x - 10

7x + 4 = 7x - 2

No solution. Contradiction.