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

Answer 1

The answers are revealed by subtracting the right side of the equation from both sides.

(a) (2x+3x-6) -(10+4x) = 0

... x -16 = 0 . . . . one solution; neither

(b) (17+5x) -(23+4x-6+x) = 0

... 0 = 0 . . . . . . . an infinite number of solutions; an identity

(c) (7x+4) -(5x+8+2x-10) = 0

... 6 = 0 . . . . . . . no solutions; a contradiction