Which equation has infinitely many solutions?
Responses
A 8x+32
= 2x + 48 x + 3 2 = 2x + 4
B 15x+53
= 5x + 215 x + 5 3 = 5x + 2
C 8x+52
= 8x + 68 x + 5 2 = 8x + 6
D 9x+63
= 3x + 2
The equation that has infinitely many solutions is option A: 8x+32 = 2x + 48 x + 3 2 = 2x + 4
The equation that has infinitely many solutions is option C.
The equation 8x + 52 = 8x + 68 is an example of an identity equation where both sides of the equation are equal regardless of the value of x. This means that any value of x will satisfy the equation, leading to infinitely many solutions.
To determine which equation has infinitely many solutions, we need to look for an equation where both sides are equal, regardless of the value of x.
Let's go through each option and simplify the equations:
A) 8x + 32 = 2x + 48
To solve for x, we will move all the x terms to one side and the constant terms to the other side:
6x = 16
Dividing both sides by 6 gives us:
x = 2
B) 15x + 53 = 5x + 215
Simplifying this equation in the same way as before, we get:
10x = 162
Dividing both sides by 10 gives us:
x = 16.2
C) 8x + 52 = 8x + 68
Here, we can see that every term is canceled out on both sides of the equation. This means that regardless of the value of x, the equation will always be true.
D) 9x + 63 = 3x + 2
Simplifying this equation, we get:
6x = -61
Dividing both sides by 6 gives us:
x = -10.16
From the simplification process, we can see that option C has infinitely many solutions because the equation simplifies to 0 = 0 -- which is true for any value of x.
Therefore, the equation with infinitely many solutions is option C: 8x + 52 = 8x + 68.