2. solve each given equation and show your work. tell whether each equation has one solution, an infinite number of solutions, or no solution. explain your answers. (a)2x + 4(x - 1) = 2 + 4x (b)25 - x = 15 - (3x + 10) (c )4x = 2x + 2x + 5(x - x)

Hello there.

(a)2x + 4(x - 1) = 2 + 4x (b)25 - x = 15 - (3x + 10) (c )4x = 2x + 2x + 5(x - x)

For (a)2x + 4(x - 1) = 2 + 4x.
 x=3
First you simplify both sides of the equation
Then just subtract 4x from both sides
After that you add 4 to both sides
Last divide both sides by 2

For 25 - x = 15 - (3x + 10).
 x=−10.
First you simplify both sides of the equation.
Then you add 3x to both sides.
Also subtract 25 from both sides.
Last divide both sides by 2.
And you get −10

For,4x = 2x + 2x + 5(x - x).
An infinite number of solutions
First, simplify both sides of the equation.
The, subtract 4x from both sides
Therefore you get 0=0

A=solution
B=solution
C=An infinite number of solutions

A
2x+4(x-1)=2+4x
we can see that everybody is divisble by 2 so divide by 2 both sides
x+2(x-1)=1+2x
distirbute
x+2x-2=1+2x
3x-2=1+2x
minus 2x both sides
x-2=1
add 2
x=3

B.
25-x=15-1(3x+10)
distribute
25-x=15-3x-10
25-x=5-3x
add 3x to both sides
25+2x=5
minus 25 both sides
2x=-20
divide both sides by 2
x=-10

C.
4x=2x+2x+5(x-x)
x-x=0
4x=2x+2x+5(0)
4x=2x+2x+0
4x=4x
divide both sides by 4
x=x
true
infinite solutions

A. x=3, 1 solution
B. x=-10, 1 solution
C. x=x, infinite solutions