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

Answer:

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

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

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

Step-by-step 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

$2x + 4 (x-1) = 2 + 4x\\2x + 4x -4  = 2 + 4x\\6x-4=2+4x\\6x-4x=2+4\\2x =6\\x= \frac{6}{2} \\x= 3$

Hence we conclude that it has one solution.

$25 - x = 15 - (3x + 10)\\25 - x = 15 -3x - 10)\\25 -x =5-3x\\-x+3x=5-25\\2x=-20\\x= \frac{-20}{2} \\x=-10$

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.