Q:

How many solutions does each equation have? Infinite, one, or none?2x + 4 (x-1) = 2 + 4x25 - x = 15 - (3x + 10)4x = 2x + 2x + 5 (x-x)

Accepted Solution

A:
Answer:[tex]2x + 4 (x-1) = 2 + 4x[/tex] has one solution[tex]25 - x = 15 - (3x + 10)[/tex] has One Solution[tex]4x = 2x + 2x + 5 (x-x)[/tex] has Infinite SolutionStep-by-step explanation:There are 3 Solutions Given1)   [tex]2x + 4 (x-1) = 2 + 4x[/tex]2)   [tex]25 - x = 15 - (3x + 10)[/tex]3)   [tex]4x = 2x + 2x + 5 (x-x)[/tex]Solving for each equation separately[tex]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[/tex]Hence we conclude that it has one solution.[tex]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[/tex]Hence we conclude that it has one solution.[tex]4x = 2x + 2x + 5 (x-x)\\4x = 4x + 5x-5x\\4x = 4x [/tex]Hence we conclude that it has Infinite Solutions.