Question

2. 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. You must complete all sections of this questions to receive full credit.
(a) 6x+4x-6=24+9x
(b) 25-4x=15-3x+10-x
(c) 4x+8=2x+7+2x-20

Answer 1

(a) 6x+4x-6=24+9x

6x+4x-6=24+9x
10x-6=24+9x
x=30
one solution, equation is "neither" identity nor contradiction

(b) 25-4x=15-3x+10-x

25-4x=15-3x+10-x
25-4x=25-4x
both sides are the same (identity)-> infinite solutions

(c) 4x+8=2x+7+2x-20
4x+8=2x+7+2x-20
4x+8=4x-13
8=-13
no solutions -> Contradiction