Answer: A. 2(7 – 4x) = 4(5 – 2x) – 6
C. 4(x + 4) = 2(2x + 5) + 6
Step-by-step explanation:
Infinitely solution means when all numbers are solutions . Checking the equations given one by one
A. 2(7- 4x ) = 4(5 - 2x ) - 6
Expanding , we have
14 - 8x = 20 - 8x - 6
14 - 8x = 20 - 6 - 8x
14 - 8x = 14 - 8x , this is just a typical example of infinitely many solutions because any value of x chosen will satisfy the equation.
B. 6(x - 9 ) = 6x - 54 + x
Expanding , we have
6x - 54 = 6x + x - 54
6x - 54 = 7x - 54
collecting the like terms
6x - 7x = -54 + 54
- x = 0
x = 0
This equation has just one solution at x = 0 , because 0 is the only value of x that will satisfy the equation
C. 4( x + 4 ) = 2 ( 2x + 5 ) + 6
4x + 16 = 4x + 10 + 6
4x + 16 = 4x + 16
This equation also have infinitely many solutions
D. 5 ( x - 8 ) + 10 = 5 ( x + 2 )
5x - 40 + 10 = 5x + 10
5x - 30 = 5x + 10
This equation has no solution.
Therefore , the equations with infinitely many solutions are equations A and C
