Question

Rocco used these steps to solve the equation 4x + 6 = 4 + 2(2x + 1). Which choice describes the meaning of his result, 6 = 6?

A.The solution is x = 6.
B.The result is not correct because Step 2 has an error.
C.All values of x make the equation true.
D.No values of x make the equation true.

Answer 1

since the x values cancel out and we are left with 6=6, all x values will work for x because it will dissapear anyway
with some modification, we can get x=x, so therefor that is true and all values work


C is answer

Answer 2

C. All values of x make the equation true.

Explanation:

A solution of an equation is a value for which the equation is true,

If after solving an equation no variable term remains,

Then, there can be two cases,

No solution : if after solving, an equation gives a false statement.

Infinitely many solutions : If after solving, the equation gives a true statement.

Here, the given equation,

`4x+6=4+2(2x+1)`

`4x+6=4+4x+2` ( By associative property )

`6=6+4x-4x`

`6 = 6`

Which is a true statement,

Hence, by the above explanations it is clear that all values of x make the equation true.

Option C is correct.