Question

How many solutions does each equation have? Infinite, one, or none?

2x + 4 (x-1) = 2 + 4x


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


4x = 2x + 2x + 5 (x-x)

Answer 1

`2x + 4 (x-1) = 2 + 4x` has one solution

`25 - x = 15 - (3x + 10)` has One Solution

`4x = 2x + 2x + 5 (x-x)` has Infinite Solution

Explanation:

There are 3 Solutions Given

1)
`2x + 4 (x-1) = 2 + 4x`

2)
`25 - x = 15 - (3x + 10)`

3)
`4x = 2x + 2x + 5 (x-x)`

Solving for each equation separately

`2x + 4 (x-1) = 2 + 4x\\2x + 4x -4  = 2 + 4x\\6x-4=2+4x\\6x-4x=2+4\\2x =6\\x= (6)/(2) \\x= 3`

Hence we conclude that it has one solution.

`25 - x = 15 - (3x + 10)\\25 - x = 15 -3x - 10)\\25 -x =5-3x\\-x+3x=5-25\\2x=-20\\x= (-20)/(2) \\x=-10`

Hence we conclude that it has one solution.

`4x = 2x + 2x + 5 (x-x)\\4x = 4x + 5x-5x\\4x = 4x`

Hence we conclude that it has Infinite Solutions.