which equations have infinitely many solutions select two that apply
a. 6 ( x - 9 ) = 6x - 54 + x
b. 5 ( x - 8 ) + 10 = 5 ( x + 2 )
c. 20 - 8x - 6 = 2 ( 7 - 4x )
d. 4 ( x + 4 ) = 2 ( 2x + 5 ) + 6
a. 6 ( x - 9 ) = 6x - 54 + x
d. 4 ( x + 4 ) = 2 ( 2x + 5 ) + 6
The equations that have infinitely many solutions are:
a. 6(x - 9) = 6x - 54 + x
d. 4(x + 4) = 2(2x + 5) + 6
To determine which equations have infinitely many solutions, we need to analyze the equations and look for any inconsistencies or contradictions.
a. 6(x - 9) = 6x - 54 + x
Let's simplify this equation:
6x - 54 = 6x - 54 + x
6x - 54 = 7x - 54
By subtracting 6x and 7x from both sides, we get:
-54 = -54
In this case, the equation is consistent and has the same value on both sides. This means that any value of x will satisfy the equation, resulting in infinitely many solutions.
b. 5(x - 8) + 10 = 5(x + 2)
Let's simplify this equation:
5x - 40 + 10 = 5x + 10
By combining like terms, we get:
5x - 30 = 5x + 10
By subtracting 5x from both sides, we get:
-30 = 10
In this case, the equation is inconsistent since -30 is not equal to 10. Therefore, there is no solution.
c. 20 - 8x - 6 = 2(7 - 4x)
Let's simplify this equation:
14 - 8x = 14 - 8x
By subtracting 14 and -8x from both sides, we get:
0 = 0
In this case, the equation is consistent and has the same value on both sides. This means that any value of x will satisfy the equation, resulting in infinitely many solutions.
d. 4(x + 4) = 2(2x + 5) + 6
Let's simplify this equation:
4x + 16 = 4x + 10 + 6
By combining like terms, we get:
4x + 16 = 4x + 16
By subtracting 4x and 16 from both sides, we get:
0 = 0
In this case, the equation is consistent and has the same value on both sides. This means that any value of x will satisfy the equation, resulting in infinitely many solutions.
To summarize, the equations (a) 6(x - 9) = 6x - 54 + x and (d) 4(x + 4) = 2(2x + 5) + 6 both have infinitely many solutions.