Question

For each equation, state whether there is no solution, one solution, or infinitely many solution. Explain your reasoning. A: 3x - 6 = 3(x - 1) - 3 B: 2x + 7 = - 2x + 7 C: 2x + 7 = 2x

Answer 1

A: Infinite

B: One

C: No Solution

Explanation:

Equation A:

`3x-6=3(x-1)-3\\\\3x-6=3x-3-3\\\\\boxed{3x-6=3x-6}`

The sides are the same. This means that the equation has infinite solutions.

Equation B:

`2x+7=-2x+7\\\\2x+7-7=-2x+7-7\\\\2x=-2x\\\\2x+2x=-2x+2x\\\\4x=0\\\\(4x=0)/(4)\\\\\boxed{x=0}`

The equation has one solution.

Equation C:

`2x+7=2x\\\\2x-2x+7=2x-2x\\\\\boxed{7\\eq 0}`

The final result is a contradiction. The equation has no solution.