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.