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) 6x+4x-6=24+9x
(B)25-4x=15 -3x+10-x
(C) 4x+8=2x+7 +2x-20

Answer 1

Solve   6x+4x-6=24+9x.  Combine all the x terms on one side and all the constants on the other:

10x-9x = 24+6, or x = 30.  ONE soution.


Solve   4x+8=2x+7 +2x-20.  Combine all the x terms on one side and all the constants on the other:  4x - 2x - 2x = 7 - 20 - 8 =>   0 = -21

This is NEVER true, so   4x+8=2x+7 +2x-20    has NO SOLUTION.

Please try solving equation B yourself.  Then I'd gladly comment on your work.