Answer:
Equations B and C have an infinite number of solutions.
B. 3x - 2 ( x + 10) = x - 20
C. 5/2x -2 = 9/2x - 2 (x + 1 )
Step-by-step explanation:
We need to check the options to find which equation has an infinite number of solutions.
A) 5x + 2 ( x - 3 ) = 5x + 2 (3 - x )
5x + 2x - 6 = 5x + 6 - 2x
5x + 2x - 5x + 2x = 6 + 6
4x = 12
x = 12/4 = 3
B) 3x - 2 ( x + 10) = x - 20
3x - 2x - 20 = x - 20
x - 20 = x - 20
x = x
C) [tex]\frac{5}{2} x - 2 = \frac{9}{2}x-2(x+1)[/tex] multiply all sides by 2
5x - 4 = 9x - 4(x+1)
5x - 4 = 9x - 4x - 4
5x - 4 = 5x - 4
5x = 5x
x = x
D) [tex]\frac{x}{2} +1=\frac{3x}{10} +3[/tex] multiply all sides by 10
5x + 10 = 3x + 30
5x - 3x = 30 - 10
2x = 20
x = 10
So, the equations which have an infinite number of solutions are B & C
